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Номер 9.3, страница 50 - гдз по геометрии 7 класс учебник Смирнов, Туяков
Авторы: Смирнов В. А., Туяков Е. А.
Тип: Учебник
Издательство: Мектеп
Год издания: 2017 - 2026
ISBN: 978-601-07-0873-0
Утверждено Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 7 классе
Глава 2. Треугольники. Параграф 9. Второй признак равенства треугольников - номер 9.3, страница 50.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129578 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/09-3" "field_display_title" => "9.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "39" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1042} "field_class" => Illuminate\Database\Eloquent\Collection {#1044} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1051} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1052} "field_country" => Illuminate\Database\Eloquent\Collection {#1054} "field_city" => Illuminate\Database\Eloquent\Collection {#1056} "field_series" => Illuminate\Database\Eloquent\Collection {#1058} "field_umk" => Illuminate\Database\Eloquent\Collection {#1059} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1063} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1064} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1065} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1067} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "39" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1068} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:2 [ 0 => App\Models\Branch {#1069 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Term {#1070 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "39" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Book {#1074 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1075} "field_class" => Illuminate\Database\Eloquent\Collection {#1077} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079} "field_author" => Illuminate\Database\Eloquent\Collection {#1081} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1084} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1085} "field_country" => Illuminate\Database\Eloquent\Collection {#1087} "field_city" => Illuminate\Database\Eloquent\Collection {#1089} "field_series" => Illuminate\Database\Eloquent\Collection {#1091} "field_umk" => Illuminate\Database\Eloquent\Collection {#1092} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1093} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1094} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1095} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1096} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1097} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1098} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1099} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1100} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1072} "field_page_start" => "39" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1073} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1102 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129369 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Второй признак равенства треугольников" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Term {#1104 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "48" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Book {#1106 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1107 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1123 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1124 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1107} "field_class" => Illuminate\Database\Eloquent\Collection {#1109} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1111} "field_author" => Illuminate\Database\Eloquent\Collection {#1113} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1116} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1117} "field_country" => Illuminate\Database\Eloquent\Collection {#1119} "field_city" => Illuminate\Database\Eloquent\Collection {#1121} "field_series" => Illuminate\Database\Eloquent\Collection {#1123} "field_umk" => Illuminate\Database\Eloquent\Collection {#1124} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1125} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1126} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1127} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1128} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1129} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1130} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1131} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1132} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1134 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "39" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129366 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_page_start" => "39" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1137} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1138} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129369 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Второй признак равенства треугольников" "field_branch_order" => "9" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1103} "field_page_start" => "48" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1105} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:3 [ 0 => App\Models\Element {#1151 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 1319641 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Edition {#1152 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5009 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1155 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1157 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5009 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1154} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1155} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1156} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1157} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1129578" "type" => "task" ] "text" => "<p><strong>9.3.</strong> На рисунках 9.4 отмечены равные отрезки и равные углы. Укажите на них равные треугольники.</p><p><strong>а)</strong></p><p>Равные треугольники: $\triangle ABC$ и $\triangle CDA$.</p><p><strong>б)</strong></p><p>Равные треугольники: $\triangle ABD$ и $\triangle CDB$.</p><p><strong>в)</strong></p><p>Равные треугольники: $\triangle ABD$ и $\triangle EBC$.</p><p><strong>г)</strong></p><p>Равные треугольники: $\triangle AOD$ и $\triangle BOC$.</p><p><strong>д)</strong></p><p>Равные треугольники: $\triangle ACD$ и $\triangle BCE$.</p><p><strong>е)</strong></p><p>Равные треугольники: $\triangle AOD$ и $\triangle BOC$.</p><p>Рис. 9.4</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1822" "height" => 1301 "path" => "/media/geometrija_07/Smirnova-u17/0-09/3-1.webp?ts=1753982276" ] ] ] #original: array:7 [ "id" => 1319641 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1160} "task" => array:2 [ "refs" => "1129578" "type" => "task" ] "text" => "<p><strong>9.3.</strong> На рисунках 9.4 отмечены равные отрезки и равные углы. Укажите на них равные треугольники.</p><p><strong>а)</strong></p><p>Равные треугольники: $\triangle ABC$ и $\triangle CDA$.</p><p><strong>б)</strong></p><p>Равные треугольники: $\triangle ABD$ и $\triangle CDB$.</p><p><strong>в)</strong></p><p>Равные треугольники: $\triangle ABD$ и $\triangle EBC$.</p><p><strong>г)</strong></p><p>Равные треугольники: $\triangle AOD$ и $\triangle BOC$.</p><p><strong>д)</strong></p><p>Равные треугольники: $\triangle ACD$ и $\triangle BCE$.</p><p><strong>е)</strong></p><p>Равные треугольники: $\triangle AOD$ и $\triangle BOC$.</p><p>Рис. 9.4</p>" "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1822" "height" => 1301 "path" => "/media/geometrija_07/Smirnova-u17/0-09/3-1.webp?ts=1753982276" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1158 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1320152 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1168 #items: array:1 [ 0 => App\Models\Edition {#1159 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5010 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1163 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1164 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1165 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5010 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1162} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Неизвестный" "field_moderator" => "pasha" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1163} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1164} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1165} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1129578" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1374" "height" => 953 "path" => "/media/geometrija_07/Smirnova-u17/1-09/3-1.webp?ts=1753982395" ] ] ] #original: array:6 [ "id" => 1320152 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1168} "task" => array:2 [ "refs" => "1129578" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "3-1.jpg" "alt" => null "width" => "1374" "height" => 953 "path" => "/media/geometrija_07/Smirnova-u17/1-09/3-1.webp?ts=1753982395" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Element {#1166 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1541431 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1176 #items: array:1 [ 0 => App\Models\Edition {#1167 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 5631 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1171 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1172 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1173 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5631 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1170} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "2-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1171} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1172} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1173} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1129578" "type" => "task" ] "text" => "<p><strong>а)</strong></p><svg width="125" height="105" viewBox="0 0 125 105" xmlns="http://www.w3.org/2000/svg"><path d="M 10 50 L 60 10 L 110 50 L 60 90 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 60 90 L 10 50" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 10 50 L 110 50" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 23.3 42.1 A 15 15 0 0 1 29.6 50" fill="none" stroke="black"></path><path d="M 23.3 57.9 A 15 15 0 0 0 29.6 50" fill="none" stroke="black"></path><path d="M 96.7 42.1 A 15 15 0 0 0 90.4 50" fill="none" stroke="black"></path><path d="M 96.7 40.1 A 17 17 0 0 0 88.4 50" fill="none" stroke="black"></path><path d="M 96.7 57.9 A 15 15 0 0 1 90.4 50" fill="none" stroke="black"></path><path d="M 96.7 59.9 A 17 17 0 0 1 88.4 50" fill="none" stroke="black"></path><text x="5" y="55">A</text><text x="55" y="8">B</text><text x="115" y="55">C</text><text x="55" y="103">D</text></svg><p>Рассмотрим треугольники $ABC$ и $ADC$.</p><p><strong>1.</strong> Сторона $AC$ — общая.</p><p><strong>2.</strong> $\angle BAC = \angle DAC$ (по условию, отмечены одной дугой).</p><p><strong>3.</strong> $\angle BCA = \angle DCA$ (по условию, отмечены двумя дугами).</p><p>Следовательно, $\triangle ABC = \triangle ADC$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).</p><p>Ответ: $\triangle ABC = \triangle ADC$.</p><p><strong>б)</strong></p><svg width="125" height="65" viewBox="0 0 125 65" xmlns="http://www.w3.org/2000/svg"><path d="M 10 50 L 30 10 L 110 10 L 90 50 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 30 10 L 90 50" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 38 16 A 15 15 0 0 1 43.6 24.3" fill="none" stroke="black"></path><path d="M 76.4 35.7 A 15 15 0 0 1 82 44" fill="none" stroke="black"></path><path d="M 28.5 44.8 A 15 15 0 0 0 34.6 37.1" fill="none" stroke="black"></path><path d="M 26.5 42.8 A 17 17 0 0 0 33.6 35.1" fill="none" stroke="black"></path><path d="M 85.4 12.9 A 15 15 0 0 0 81.3 21" fill="none" stroke="black"></path><path d="M 87.4 14.9 A 17 17 0 0 0 82.3 23" fill="none" stroke="black"></path><text x="5" y="55">A</text><text x="25" y="8">B</text><text x="115" y="15">C</text><text x="95" y="55">D</text></svg><p>Рассмотрим треугольники $ABD$ и $CDB$.</p><p><strong>1.</strong> Сторона $BD$ — общая.</p><p><strong>2.</strong> $\angle ABD = \angle CDB$ (по условию, отмечены одной дугой).</p><p><strong>3.</strong> $\angle ADB = \angle CBD$ (по условию, отмечены двумя дугами).</p><p>Следовательно, $\triangle ABD = \triangle CDB$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).</p><p>Ответ: $\triangle ABD = \triangle CDB$.</p><p><strong>в)</strong></p><svg width="125" height="105" viewBox="0 0 125 105" xmlns="http://www.w3.org/2000/svg"><path d="M 10 90 L 110 10" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 10 10 L 110 90" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 30.9 25.9 A 30 30 0 0 1 14.5 40" fill="none" stroke="black"></path><path d="M 90.9 75.9 A 30 30 0 0 0 105.5 60" fill="none" stroke="black"></path><path d="M 30 30 L 35 34" stroke="black"></path><path d="M 30 34 L 35 30" stroke="black"></path><path d="M 85 70 L 90 74" stroke="black"></path><path d="M 85 74 L 90 70" stroke="black"></path><text x="5" y="95">A</text><text x="55" y="48">B</text><text x="115" y="15">C</text><text x="5" y="15">D</text><text x="115" y="95">E</text></svg><p>Рассмотрим треугольники $ABD$ и $CBE$.</p><p><strong>1.</strong> $\angle ABD = \angle CBE$ как вертикальные углы.</p><p><strong>2.</strong> По условию на рисунке отмечено, что $DB = EB$ (штрихами) и $\angle D = \angle E$ (дугами), т.е. $\angle ADB = \angle CEB$.</p><p>Следовательно, $\triangle ABD = \triangle CBE$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).</p><p>Ответ: $\triangle ABD = \triangle CBE$.</p><p><strong>г)</strong></p><svg width="125" height="95" viewBox="0 0 125 95" xmlns="http://www.w3.org/2000/svg"><path d="M 10 80 L 110 80 L 90 20 L 30 20 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 10 80 L 90 20" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 110 80 L 30 20" stroke="green" fill="none" stroke-width="1.5"></path><line x1="18.5" y1="52" x2="21.5" y2="48" stroke="black"></line><line x1="98.5" y1="48" x2="101.5" y2="52" stroke="black"></line><path d="M 25 80 A 15 15 0 0 1 18.2 67.2" fill="none" stroke="black"></path><path d="M 95 80 A 15 15 0 0 0 101.8 67.2" fill="none" stroke="black"></path><text x="5" y="85">A</text><text x="115" y="85">B</text><text x="95" y="20">C</text><text x="25" y="20">D</text><text x="60" y="55">O</text></svg><p>Рассмотрим треугольники $DAB$ и $CBA$.</p><p><strong>1.</strong> Сторона $AB$ — общая.</p><p><strong>2.</strong> $AD = BC$ (по условию, отмечены штрихами).</p><p><strong>3.</strong> $\angle DAB = \angle CBA$ (по условию, отмечены дугами).</p><p>Следовательно, $\triangle DAB = \triangle CBA$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).</p><p>Ответ: $\triangle DAB = \triangle CBA$.</p><p><strong>д)</strong></p><svg width="125" height="105" viewBox="0 0 125 105" xmlns="http://www.w3.org/2000/svg"><path d="M 10 90 L 110 90 L 60 10 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 10 90 L 76.7 36.7" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 110 90 L 43.3 36.7" stroke="green" fill="none" stroke-width="1.5"></path><line x1="53" y1="23" x2="51" y2="26" stroke="black"></line><line x1="67" y1="23" x2="69" y2="26" stroke="black"></line><line x1="24" y1="65" x2="26" y2="62" stroke="black"></line><line x1="22" y1="64" x2="24" y2="61" stroke="black"></line><line x1="94" y1="65" x2="96" y2="62" stroke="black"></line><line x1="92" y1="64" x2="94" y2="61" stroke="black"></line><text x="5" y="95">A</text><text x="115" y="95">B</text><text x="55" y="8">C</text><text x="80" y="38">D</text><text x="35" y="38">E</text><text x="60" y="55">O</text></svg><p>Рассмотрим треугольники $ACD$ и $BCE$.</p><p><strong>1.</strong> По условию $CE = CD$ (отмечены одним штрихом) и $AE = BD$ (отмечены двумя штрихами). Сложив эти равенства, получаем $CE + AE = CD + BD$, то есть $AC = BC$.</p><p><strong>2.</strong> Угол $C$ — общий для этих треугольников.</p><p>Таким образом, в треугольниках $ACD$ и $BCE$ стороны $AC$ и $CD$ равны сторонам $BC$ и $CE$, а угол между ними ($C$) общий. Следовательно, $\triangle ACD = \triangle BCE$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).</p><p>Ответ: $\triangle ACD = \triangle BCE$.</p><p><strong>е)</strong></p><svg width="125" height="95" viewBox="0 0 125 95" xmlns="http://www.w3.org/2000/svg"><path d="M 30 80 L 90 80 L 110 20 L 10 20 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 30 80 L 110 20" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 90 80 L 10 20" stroke="red" fill="none" stroke-width="1.5"></path><line x1="18.5" y1="52" x2="21.5" y2="48" stroke="black"></line><line x1="98.5" y1="48" x2="101.5" y2="52" stroke="black"></line><path d="M 18.2 27.2 A 15 15 0 0 1 30 30" fill="none" stroke="black"></path><path d="M 101.8 27.2 A 15 15 0 0 0 90 30" fill="none" stroke="black"></path><text x="25" y="85">A</text><text x="95" y="85">B</text><text x="115" y="20">C</text><text x="5" y="20">D</text><text x="60" y="55">O</text></svg><p>Рассмотрим треугольники $ADC$ и $BCD$.</p><p><strong>1.</strong> Сторона $DC$ — общая.</p><p><strong>2.</strong> $AD = BC$ (по условию, отмечены штрихами).</p><p><strong>3.</strong> $\angle ADC = \angle BCD$ (по условию, отмечены дугами).</p><p>Следовательно, $\triangle ADC = \triangle BCD$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).</p><p>Ответ: $\triangle ADC = \triangle BCD$.</p>" ] #original: array:6 [ "id" => 1541431 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1176} "task" => array:2 [ "refs" => "1129578" "type" => "task" ] "text" => "<p><strong>а)</strong></p><svg width="125" height="105" viewBox="0 0 125 105" xmlns="http://www.w3.org/2000/svg"><path d="M 10 50 L 60 10 L 110 50 L 60 90 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 60 90 L 10 50" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 10 50 L 110 50" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 23.3 42.1 A 15 15 0 0 1 29.6 50" fill="none" stroke="black"></path><path d="M 23.3 57.9 A 15 15 0 0 0 29.6 50" fill="none" stroke="black"></path><path d="M 96.7 42.1 A 15 15 0 0 0 90.4 50" fill="none" stroke="black"></path><path d="M 96.7 40.1 A 17 17 0 0 0 88.4 50" fill="none" stroke="black"></path><path d="M 96.7 57.9 A 15 15 0 0 1 90.4 50" fill="none" stroke="black"></path><path d="M 96.7 59.9 A 17 17 0 0 1 88.4 50" fill="none" stroke="black"></path><text x="5" y="55">A</text><text x="55" y="8">B</text><text x="115" y="55">C</text><text x="55" y="103">D</text></svg><p>Рассмотрим треугольники $ABC$ и $ADC$.</p><p><strong>1.</strong> Сторона $AC$ — общая.</p><p><strong>2.</strong> $\angle BAC = \angle DAC$ (по условию, отмечены одной дугой).</p><p><strong>3.</strong> $\angle BCA = \angle DCA$ (по условию, отмечены двумя дугами).</p><p>Следовательно, $\triangle ABC = \triangle ADC$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).</p><p>Ответ: $\triangle ABC = \triangle ADC$.</p><p><strong>б)</strong></p><svg width="125" height="65" viewBox="0 0 125 65" xmlns="http://www.w3.org/2000/svg"><path d="M 10 50 L 30 10 L 110 10 L 90 50 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 30 10 L 90 50" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 38 16 A 15 15 0 0 1 43.6 24.3" fill="none" stroke="black"></path><path d="M 76.4 35.7 A 15 15 0 0 1 82 44" fill="none" stroke="black"></path><path d="M 28.5 44.8 A 15 15 0 0 0 34.6 37.1" fill="none" stroke="black"></path><path d="M 26.5 42.8 A 17 17 0 0 0 33.6 35.1" fill="none" stroke="black"></path><path d="M 85.4 12.9 A 15 15 0 0 0 81.3 21" fill="none" stroke="black"></path><path d="M 87.4 14.9 A 17 17 0 0 0 82.3 23" fill="none" stroke="black"></path><text x="5" y="55">A</text><text x="25" y="8">B</text><text x="115" y="15">C</text><text x="95" y="55">D</text></svg><p>Рассмотрим треугольники $ABD$ и $CDB$.</p><p><strong>1.</strong> Сторона $BD$ — общая.</p><p><strong>2.</strong> $\angle ABD = \angle CDB$ (по условию, отмечены одной дугой).</p><p><strong>3.</strong> $\angle ADB = \angle CBD$ (по условию, отмечены двумя дугами).</p><p>Следовательно, $\triangle ABD = \triangle CDB$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).</p><p>Ответ: $\triangle ABD = \triangle CDB$.</p><p><strong>в)</strong></p><svg width="125" height="105" viewBox="0 0 125 105" xmlns="http://www.w3.org/2000/svg"><path d="M 10 90 L 110 10" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 10 10 L 110 90" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 30.9 25.9 A 30 30 0 0 1 14.5 40" fill="none" stroke="black"></path><path d="M 90.9 75.9 A 30 30 0 0 0 105.5 60" fill="none" stroke="black"></path><path d="M 30 30 L 35 34" stroke="black"></path><path d="M 30 34 L 35 30" stroke="black"></path><path d="M 85 70 L 90 74" stroke="black"></path><path d="M 85 74 L 90 70" stroke="black"></path><text x="5" y="95">A</text><text x="55" y="48">B</text><text x="115" y="15">C</text><text x="5" y="15">D</text><text x="115" y="95">E</text></svg><p>Рассмотрим треугольники $ABD$ и $CBE$.</p><p><strong>1.</strong> $\angle ABD = \angle CBE$ как вертикальные углы.</p><p><strong>2.</strong> По условию на рисунке отмечено, что $DB = EB$ (штрихами) и $\angle D = \angle E$ (дугами), т.е. $\angle ADB = \angle CEB$.</p><p>Следовательно, $\triangle ABD = \triangle CBE$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).</p><p>Ответ: $\triangle ABD = \triangle CBE$.</p><p><strong>г)</strong></p><svg width="125" height="95" viewBox="0 0 125 95" xmlns="http://www.w3.org/2000/svg"><path d="M 10 80 L 110 80 L 90 20 L 30 20 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 10 80 L 90 20" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 110 80 L 30 20" stroke="green" fill="none" stroke-width="1.5"></path><line x1="18.5" y1="52" x2="21.5" y2="48" stroke="black"></line><line x1="98.5" y1="48" x2="101.5" y2="52" stroke="black"></line><path d="M 25 80 A 15 15 0 0 1 18.2 67.2" fill="none" stroke="black"></path><path d="M 95 80 A 15 15 0 0 0 101.8 67.2" fill="none" stroke="black"></path><text x="5" y="85">A</text><text x="115" y="85">B</text><text x="95" y="20">C</text><text x="25" y="20">D</text><text x="60" y="55">O</text></svg><p>Рассмотрим треугольники $DAB$ и $CBA$.</p><p><strong>1.</strong> Сторона $AB$ — общая.</p><p><strong>2.</strong> $AD = BC$ (по условию, отмечены штрихами).</p><p><strong>3.</strong> $\angle DAB = \angle CBA$ (по условию, отмечены дугами).</p><p>Следовательно, $\triangle DAB = \triangle CBA$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).</p><p>Ответ: $\triangle DAB = \triangle CBA$.</p><p><strong>д)</strong></p><svg width="125" height="105" viewBox="0 0 125 105" xmlns="http://www.w3.org/2000/svg"><path d="M 10 90 L 110 90 L 60 10 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 10 90 L 76.7 36.7" stroke="green" fill="none" stroke-width="1.5"></path><path d="M 110 90 L 43.3 36.7" stroke="green" fill="none" stroke-width="1.5"></path><line x1="53" y1="23" x2="51" y2="26" stroke="black"></line><line x1="67" y1="23" x2="69" y2="26" stroke="black"></line><line x1="24" y1="65" x2="26" y2="62" stroke="black"></line><line x1="22" y1="64" x2="24" y2="61" stroke="black"></line><line x1="94" y1="65" x2="96" y2="62" stroke="black"></line><line x1="92" y1="64" x2="94" y2="61" stroke="black"></line><text x="5" y="95">A</text><text x="115" y="95">B</text><text x="55" y="8">C</text><text x="80" y="38">D</text><text x="35" y="38">E</text><text x="60" y="55">O</text></svg><p>Рассмотрим треугольники $ACD$ и $BCE$.</p><p><strong>1.</strong> По условию $CE = CD$ (отмечены одним штрихом) и $AE = BD$ (отмечены двумя штрихами). Сложив эти равенства, получаем $CE + AE = CD + BD$, то есть $AC = BC$.</p><p><strong>2.</strong> Угол $C$ — общий для этих треугольников.</p><p>Таким образом, в треугольниках $ACD$ и $BCE$ стороны $AC$ и $CD$ равны сторонам $BC$ и $CE$, а угол между ними ($C$) общий. Следовательно, $\triangle ACD = \triangle BCE$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).</p><p>Ответ: $\triangle ACD = \triangle BCE$.</p><p><strong>е)</strong></p><svg width="125" height="95" viewBox="0 0 125 95" xmlns="http://www.w3.org/2000/svg"><path d="M 30 80 L 90 80 L 110 20 L 10 20 Z" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 30 80 L 110 20" stroke="red" fill="none" stroke-width="1.5"></path><path d="M 90 80 L 10 20" stroke="red" fill="none" stroke-width="1.5"></path><line x1="18.5" y1="52" x2="21.5" y2="48" stroke="black"></line><line x1="98.5" y1="48" x2="101.5" y2="52" stroke="black"></line><path d="M 18.2 27.2 A 15 15 0 0 1 30 30" fill="none" stroke="black"></path><path d="M 101.8 27.2 A 15 15 0 0 0 90 30" fill="none" stroke="black"></path><text x="25" y="85">A</text><text x="95" y="85">B</text><text x="115" y="20">C</text><text x="5" y="20">D</text><text x="60" y="55">O</text></svg><p>Рассмотрим треугольники $ADC$ и $BCD$.</p><p><strong>1.</strong> Сторона $DC$ — общая.</p><p><strong>2.</strong> $AD = BC$ (по условию, отмечены штрихами).</p><p><strong>3.</strong> $\angle ADC = \angle BCD$ (по условию, отмечены дугами).</p><p>Следовательно, $\triangle ADC = \triangle BCD$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).</p><p>Ответ: $\triangle ADC = \triangle BCD$.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1129579" "type" => "task" ] "previous" => array:2 [ "refs" => "1129577" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Book {#1148 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Term {#1140 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6477 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "геометрию" "field_creative_case" => "геометрией" "field_dative_case" => "геометрии" "field_genitive_case" => "геометрии" "field_nominative_case" => "геометрия" "field_prepositional_case" => "геометрии" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #original: array:10 [ "id" => 6477 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "геометрию" "field_creative_case" => "геометрией" "field_dative_case" => "геометрии" "field_genitive_case" => "геометрии" "field_nominative_case" => "геометрия" "field_prepositional_case" => "геометрии" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Term {#1149 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ "field_accusative_case" => "седьмой" "field_creative_case" => "седьмым" …4 ] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Term {#1143 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ …6] "field_translit" => "mektep" ] #original: array:6 [ "id" => 6996 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ …6] "field_translit" => "mektep" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:2 [ 0 => App\Models\Term {#1144 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Смирнов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Смирнов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1174 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 7017 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Туяков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Есенкельды" "field_patronymic" => "Алыбаевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 7017 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Туяков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Есенкельды" "field_patronymic" => "Алыбаевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1175 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Term {#1178 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1179 #items: array:1 [ 0 => App\Models\Term {#1180 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Term {#1182 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1183 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1184 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1185 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1186 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1187 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1188 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1189 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1190 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1191 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1141} "field_class" => Illuminate\Database\Eloquent\Collection {#1147} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1145} "field_author" => Illuminate\Database\Eloquent\Collection {#1146} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1175} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1177} "field_country" => Illuminate\Database\Eloquent\Collection {#1179} "field_city" => Illuminate\Database\Eloquent\Collection {#1181} "field_series" => Illuminate\Database\Eloquent\Collection {#1183} "field_umk" => Illuminate\Database\Eloquent\Collection {#1184} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1185} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1186} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1187} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1188} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2017" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 7 класса общеобразовательной школы" "field_allowed" => "Утверждено Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "528" "field_priority" => "2" "field_default_folder" => "/geometrija_07/Smirnova-u17/" "field_isbn" => "978-601-07-0873-0" "field_cover" => array:1 [ 0 => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp?ts=1753259592" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1189} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1190} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1191} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1192} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\BookPage {#1199 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 1114367 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-50" "field_display_title" => "50" "field_folder" => "1" "field_image_name" => "50" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202 #items: array:1 [ 0 => App\Models\Book {#1148} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1203 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Element {#1212 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1290554 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1290554 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1114368" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114366" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1370 #items: array:2 [ 0 => App\Models\Task {#1378 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129578 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/09-3" "field_display_title" => "9.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1379 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1380 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1382 …2} "content" => Illuminate\Database\Eloquent\Collection {#1383 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1384 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129578 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/09-3" "field_display_title" => "9.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1379 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1380 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1382 …2} "content" => Illuminate\Database\Eloquent\Collection {#1383 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1384 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1385 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1129579 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/09-4" "field_display_title" => "9.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1386 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1387 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1388 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1389 …2} "content" => Illuminate\Database\Eloquent\Collection {#1392 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1398 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129579 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/09-4" "field_display_title" => "9.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1386 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1387 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1388 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1389 …2} "content" => Illuminate\Database\Eloquent\Collection {#1392 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1398 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1114367 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-50" "field_display_title" => "50" "field_folder" => "1" "field_image_name" => "50" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1201} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1202} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "edition_groups" => Illuminate\Database\Eloquent\Collection {#1203} "content" => Illuminate\Database\Eloquent\Collection {#1213} "next" => array:2 [ "refs" => "1114368" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114366" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1370} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1129578 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "50" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/09-3" "field_display_title" => "9.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1071} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1139} "content" => Illuminate\Database\Eloquent\Collection {#1142} "next" => array:2 [ "refs" => "1129579" "type" => "task" ] "previous" => array:2 [ "refs" => "1129577" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1195} "page" => array:2 [ "refs" => "1114367" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№9.3 (с. 50)
Условие. №9.3 (с. 50)
скриншот условия
9.3. На рисунках 9.4 отмечены равные отрезки и равные углы. Укажите на них равные треугольники.
а)
Равные треугольники: $\triangle ABC$ и $\triangle CDA$.
б)
Равные треугольники: $\triangle ABD$ и $\triangle CDB$.
в)
Равные треугольники: $\triangle ABD$ и $\triangle EBC$.
г)
Равные треугольники: $\triangle AOD$ и $\triangle BOC$.
д)
Равные треугольники: $\triangle ACD$ и $\triangle BCE$.
е)
Равные треугольники: $\triangle AOD$ и $\triangle BOC$.
Рис. 9.4
Решение. №9.3 (с. 50)
Решение 2. №9.3 (с. 50)
а)
Рассмотрим треугольники $ABC$ и $ADC$.
1. Сторона $AC$ — общая.
2. $\angle BAC = \angle DAC$ (по условию, отмечены одной дугой).
3. $\angle BCA = \angle DCA$ (по условию, отмечены двумя дугами).
Следовательно, $\triangle ABC = \triangle ADC$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).
Ответ: $\triangle ABC = \triangle ADC$.
б)
Рассмотрим треугольники $ABD$ и $CDB$.
1. Сторона $BD$ — общая.
2. $\angle ABD = \angle CDB$ (по условию, отмечены одной дугой).
3. $\angle ADB = \angle CBD$ (по условию, отмечены двумя дугами).
Следовательно, $\triangle ABD = \triangle CDB$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).
Ответ: $\triangle ABD = \triangle CDB$.
в)
Рассмотрим треугольники $ABD$ и $CBE$.
1. $\angle ABD = \angle CBE$ как вертикальные углы.
2. По условию на рисунке отмечено, что $DB = EB$ (штрихами) и $\angle D = \angle E$ (дугами), т.е. $\angle ADB = \angle CEB$.
Следовательно, $\triangle ABD = \triangle CBE$ по второму признаку равенства треугольников (по стороне и двум прилежащим к ней углам).
Ответ: $\triangle ABD = \triangle CBE$.
г)
Рассмотрим треугольники $DAB$ и $CBA$.
1. Сторона $AB$ — общая.
2. $AD = BC$ (по условию, отмечены штрихами).
3. $\angle DAB = \angle CBA$ (по условию, отмечены дугами).
Следовательно, $\triangle DAB = \triangle CBA$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).
Ответ: $\triangle DAB = \triangle CBA$.
д)
Рассмотрим треугольники $ACD$ и $BCE$.
1. По условию $CE = CD$ (отмечены одним штрихом) и $AE = BD$ (отмечены двумя штрихами). Сложив эти равенства, получаем $CE + AE = CD + BD$, то есть $AC = BC$.
2. Угол $C$ — общий для этих треугольников.
Таким образом, в треугольниках $ACD$ и $BCE$ стороны $AC$ и $CD$ равны сторонам $BC$ и $CE$, а угол между ними ($C$) общий. Следовательно, $\triangle ACD = \triangle BCE$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).
Ответ: $\triangle ACD = \triangle BCE$.
е)
Рассмотрим треугольники $ADC$ и $BCD$.
1. Сторона $DC$ — общая.
2. $AD = BC$ (по условию, отмечены штрихами).
3. $\angle ADC = \angle BCD$ (по условию, отмечены дугами).
Следовательно, $\triangle ADC = \triangle BCD$ по первому признаку равенства треугольников (по двум сторонам и углу между ними).
Ответ: $\triangle ADC = \triangle BCD$.
Другие задания:
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