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Номер 3.16, страница 49 - гдз по геометрии 7 класс учебник Шыныбеков, Шыныбеков
Авторы: Шыныбеков А. Н., Шыныбеков Д. А.
Тип: Учебник
Издательство: Атамұра
Год издания: 2017 - 2026
ISBN: 978-601-306-749-0
Рекомендовано Министерством образования и науки Республики Казахстан
Популярные ГДЗ в 7 классе
Раздел 3. Взаимное расположение прямых. 3.1. Признаки параллельности прямых - номер 3.16, страница 49.
App\Models\Task {#1003 // 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" => 1122204 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-16" "field_display_title" => "3.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1009 #items: array:1 [ 0 => App\Models\Term {#1008 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1007 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1018 #items: array:1 [ 0 => App\Models\Branch {#1017 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1122025 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Взаимное расположение прямых" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1022 #items: array:1 [ 0 => App\Models\Term {#1019 #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" => 30 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Раздел" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 30 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Раздел" "field_cases" => array:6 [ …6] "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" => "42" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Book {#1021 #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" => 2583 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1023 #items: array:1 [ 0 => App\Models\Term {#1020 #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" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "geometrija" ] #original: array:10 [ "id" => 6477 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Геометрия" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "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 {#1024 #items: array:1 [ 0 => App\Models\Term {#1025 #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" => "2026-04-08 17:28:58" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-08 17:28:58" "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 {#1026 #items: array:1 [ 0 => App\Models\Term {#1027 #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" => 6991 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Атамұра" "field_cases" => array:6 [ …6] "field_translit" => "atamu'ra" ] #original: array:6 [ "id" => 6991 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Атамұра" "field_cases" => array:6 [ …6] "field_translit" => "atamu'ra" ] #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 {#1028 #items: array:2 [ 0 => App\Models\Term {#1029 #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" => 6992 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Шыныбеков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абдухали" "field_patronymic" => "Насырович" "field_surname_rp" => null ] #original: array:12 [ "id" => 6992 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Шыныбеков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абдухали" "field_patronymic" => "Насырович" "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 {#1030 #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" => 6993 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Шыныбеков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Данияр" "field_patronymic" => "Абдухалиевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 6993 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Шыныбеков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Данияр" "field_patronymic" => "Абдухалиевич" "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 {#1031 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1032 #items: array:1 [ 0 => App\Models\Term {#1033 #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" => "2026-04-08 17:28:58" "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" => "2026-04-08 17:28:58" "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 {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #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" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-08 17:28:58" "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 {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #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" => "2026-04-08 17:28:58" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-08 17:28:58" "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 {#1038 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1040 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1041 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1043 #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" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "337" "field_priority" => "4" "field_default_folder" => "/geometrija_07/Shynybekov-u17/" "field_isbn" => "978-601-306-749-0" "field_cover" => array:2 [ 0 => "/media/geometrija_07/Shynybekov-u17/covers/cover1.webp" 1 => "/media/geometrija_07/Shynybekov-u17/covers/cover2.webp" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/geometrija_07/Shynybekov-u17/covers/cover1.webp" "alt" => "" "width" => "1676" "height" => "2498" ] 1 => array:4 [ "path" => "/media/geometrija_07/Shynybekov-u17/covers/cover2.webp" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1044 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1045 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1046 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/shynybekov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1047 #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" => 2583 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1023} "field_class" => Illuminate\Database\Eloquent\Collection {#1024} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1026} "field_author" => Illuminate\Database\Eloquent\Collection {#1028} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1031} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1032} "field_country" => Illuminate\Database\Eloquent\Collection {#1034} "field_city" => Illuminate\Database\Eloquent\Collection {#1036} "field_series" => Illuminate\Database\Eloquent\Collection {#1038} "field_umk" => Illuminate\Database\Eloquent\Collection {#1039} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1040} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1041} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1042} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1043} "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" => "Рекомендовано Министерством образования и науки Республики Казахстан" "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "337" "field_priority" => "4" "field_default_folder" => "/geometrija_07/Shynybekov-u17/" "field_isbn" => "978-601-306-749-0" "field_cover" => array:2 [ 0 => "/media/geometrija_07/Shynybekov-u17/covers/cover1.webp" 1 => "/media/geometrija_07/Shynybekov-u17/covers/cover2.webp" ] "field_cover_alts" => array:2 [ 0 => "" 1 => "" ] "field_covers" => array:2 [ 0 => array:4 [ "path" => "/media/geometrija_07/Shynybekov-u17/covers/cover1.webp" "alt" => "" "width" => "1676" "height" => "2498" ] 1 => array:4 [ "path" => "/media/geometrija_07/Shynybekov-u17/covers/cover2.webp" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1044} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1045} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1046} "field_url" => "/7-klass/geometrija/shynybekov-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1047} "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 {#1048 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1122025 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Взаимное расположение прямых" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1022} "field_page_start" => "42" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1050} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1048} ] #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 {#1077 #items: array:2 [ 0 => App\Models\Branch {#1085 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1122025 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Взаимное расположение прямых" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1086 #items: array:1 [ 0 => App\Models\Term {#1019} ] #escapeWhenCastingToString: false } "field_page_start" => "42" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Book {#1021} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1088 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1122025 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "Взаимное расположение прямых" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1086} "field_page_start" => "42" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1087} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1088} ] #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 {#1089 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:23 [ "id" => 1122026 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "3.1. Признаки параллельности прямых" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "42" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Book {#1021} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1092 #items: array:1 [ 0 => App\Models\Branch {#1017} ] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1122026 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_display_title" => "3.1. Признаки параллельности прямых" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1090} "field_page_start" => "42" "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" => [] "book" => Illuminate\Database\Eloquent\Collection {#1091} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1092} ] #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 {#1010 #items: array:4 [ 0 => App\Models\Element {#1066 #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" => 1303963 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => App\Models\Edition {#1065 #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" => 5003 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие rus" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1062 …2} "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" => "0rus-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5003 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие rus" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1062 …2} "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" => "0rus-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1061 …2} "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" => "1122204" "type" => "task" ] "text" => "<p><strong>3.16.</strong> Найдите внешний угол при третьей вершине треугольника, если два других угла равны:</p><p><strong>1</strong>) $54^\circ$ и $36^\circ$;</p><p><strong>2</strong>) $42^\circ$ и $78^\circ$;</p><p><strong>3</strong>) $65^\circ$ и $35^\circ$;</p><p><strong>4</strong>) $33^\circ$ и $120^\circ$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1456" "height" => 259 "path" => "/media/geometrija_07/Shynybekov-u17/0rus-3/16-1.webp" ] ] ] #original: array:7 [ "id" => 1303963 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1057} "task" => array:2 [ "refs" => "1122204" "type" => "task" ] "text" => "<p><strong>3.16.</strong> Найдите внешний угол при третьей вершине треугольника, если два других угла равны:</p><p><strong>1</strong>) $54^\circ$ и $36^\circ$;</p><p><strong>2</strong>) $42^\circ$ и $78^\circ$;</p><p><strong>3</strong>) $65^\circ$ и $35^\circ$;</p><p><strong>4</strong>) $33^\circ$ и $120^\circ$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1456" "height" => 259 "path" => "/media/geometrija_07/Shynybekov-u17/0rus-3/16-1.webp" ] ] ] #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 {#1058 #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" => 1304207 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1015 #items: array:1 [ 0 => App\Models\Edition {#1059 #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" => 5004 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие kz" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0kz-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5004 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Условие kz" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_content_type" => "free" "field_content_mode" => "image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "pasha" "field_edition_type" => "statement" "field_root_dir" => "0kz-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1053 …2} "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" => "1122204" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1487" "height" => 260 "path" => "/media/geometrija_07/Shynybekov-u17/0kz-3/16-1.webp" ] ] ] #original: array:6 [ "id" => 1304207 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1015} "task" => array:2 [ "refs" => "1122204" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1487" "height" => 260 "path" => "/media/geometrija_07/Shynybekov-u17/0kz-3/16-1.webp" ] ] ] #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 {#1049 #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" => 1304601 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:1 [ 0 => App\Models\Edition {#1051 #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" => 5005 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1006 …2} "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 {#1011 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5005 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1006 …2} "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 {#1011 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1075 …2} "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" => "1122204" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1848" "height" => 662 "path" => "/media/geometrija_07/Shynybekov-u17/1-3/16-1.webp" ] 1 => array:5 [ "name" => "16-2.jpg" "alt" => null "width" => "1848" "height" => 927 "path" => "/media/geometrija_07/Shynybekov-u17/1-3/16-2.webp" ] ] ] #original: array:6 [ "id" => 1304601 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1078} "task" => array:2 [ "refs" => "1122204" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "16-1.jpg" "alt" => null "width" => "1848" "height" => 662 "path" => "/media/geometrija_07/Shynybekov-u17/1-3/16-1.webp" ] 1 => array:5 [ "name" => "16-2.jpg" "alt" => null "width" => "1848" "height" => 927 "path" => "/media/geometrija_07/Shynybekov-u17/1-3/16-2.webp" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Element {#1084 #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" => 1480517 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1080 #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" => 5433 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение 2 rus" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079 …2} "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 {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5433 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "title" => "Решение 2 rus" "field_order" => "4" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079 …2} "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 {#1093 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 …2} "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" => "1122204" "type" => "task" ] "text" => "<p>Для решения этой задачи используется свойство внешнего угла треугольника. Теорема о внешнем угле треугольника гласит, что внешний угол при любой вершине треугольника равен сумме двух внутренних углов, не смежных с ним.</p><p>Следовательно, для нахождения внешнего угла при третьей вершине нужно просто сложить два данных угла.</p><p><strong>1)</strong> Даны углы $54^\circ$ и $36^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$54^\circ + 36^\circ = 90^\circ$.</p><p>Ответ: $90^\circ$.</p><p><strong>2)</strong> Даны углы $42^\circ$ и $78^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$42^\circ + 78^\circ = 120^\circ$.</p><p>Ответ: $120^\circ$.</p><p><strong>3)</strong> Даны углы $65^\circ$ и $35^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$65^\circ + 35^\circ = 100^\circ$.</p><p>Ответ: $100^\circ$.</p><p><strong>4)</strong> Даны углы $33^\circ$ и $120^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$33^\circ + 120^\circ = 153^\circ$.</p><p>Ответ: $153^\circ$.</p>" ] #original: array:6 [ "id" => 1480517 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1122204" "type" => "task" ] "text" => "<p>Для решения этой задачи используется свойство внешнего угла треугольника. Теорема о внешнем угле треугольника гласит, что внешний угол при любой вершине треугольника равен сумме двух внутренних углов, не смежных с ним.</p><p>Следовательно, для нахождения внешнего угла при третьей вершине нужно просто сложить два данных угла.</p><p><strong>1)</strong> Даны углы $54^\circ$ и $36^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$54^\circ + 36^\circ = 90^\circ$.</p><p>Ответ: $90^\circ$.</p><p><strong>2)</strong> Даны углы $42^\circ$ и $78^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$42^\circ + 78^\circ = 120^\circ$.</p><p>Ответ: $120^\circ$.</p><p><strong>3)</strong> Даны углы $65^\circ$ и $35^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$65^\circ + 35^\circ = 100^\circ$.</p><p>Ответ: $100^\circ$.</p><p><strong>4)</strong> Даны углы $33^\circ$ и $120^\circ$.</p><p>Находим внешний угол при третьей вершине как сумму этих двух углов:</p><p>$33^\circ + 120^\circ = 153^\circ$.</p><p>Ответ: $153^\circ$.</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" => "1122205" "type" => "task" ] "previous" => array:2 [ "refs" => "1122203" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Book {#1021} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1014 #items: array:1 [ 0 => App\Models\BookPage {#1073 #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" => 1114155 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/page-49" "field_display_title" => "49" "field_folder" => "folder1" "field_image_name" => "49" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1072 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1012 #items: array:1 [ 0 => App\Models\Book {#1021} ] #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 {#1096 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1099 #items: array:2 [ 0 => App\Models\Element {#1108 #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" => 1290163 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1290163 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1109 …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 => "*" ] } 1 => App\Models\Element {#1110 #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" => 1290221 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1290221 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111 …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" => "1114156" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114154" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:12 [ 0 => App\Models\Task {#1204 #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" => 1122202 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-14" "field_display_title" => "3.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1205 …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 {#1206 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1207 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1208 …2} "content" => Illuminate\Database\Eloquent\Collection {#1210 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1219 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122202 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-14" "field_display_title" => "3.14" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1205 …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 {#1206 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1207 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1208 …2} "content" => Illuminate\Database\Eloquent\Collection {#1210 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1219 …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 {#1211 #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" => 1122203 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-15" "field_display_title" => "3.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1209 …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 {#1217 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1216 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1218 …2} "content" => Illuminate\Database\Eloquent\Collection {#1212 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1235 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122203 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-15" "field_display_title" => "3.15" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1209 …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 {#1217 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1216 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1218 …2} "content" => Illuminate\Database\Eloquent\Collection {#1212 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1235 …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 => "*" ] } 2 => App\Models\Task {#1215 #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" => 1122204 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-16" "field_display_title" => "3.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1233 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1232 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1234 …2} "content" => Illuminate\Database\Eloquent\Collection {#1230 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1213 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122204 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-16" "field_display_title" => "3.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1214 …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 {#1233 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1232 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1234 …2} "content" => Illuminate\Database\Eloquent\Collection {#1230 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1213 …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 => "*" ] } 3 => App\Models\Task {#1231 #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" => 1122205 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-17" "field_display_title" => "3.17" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229 …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 {#1245 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1246 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1247 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1258 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122205 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-17" "field_display_title" => "3.17" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1229 …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 {#1245 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1246 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1247 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1258 …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 => "*" ] } 4 => App\Models\Task {#1250 #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" => 1122206 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-18" "field_display_title" => "3.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1248 …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 {#1256 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1274 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122206 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-18" "field_display_title" => "3.18" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1248 …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 {#1256 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1257 …2} "content" => Illuminate\Database\Eloquent\Collection {#1251 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1274 …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 => "*" ] } 5 => App\Models\Task {#1254 #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" => 1122207 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-19" "field_display_title" => "3.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1253 …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 {#1272 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1271 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1273 …2} "content" => Illuminate\Database\Eloquent\Collection {#1252 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1290 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122207 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-19" "field_display_title" => "3.19" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1253 …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 {#1272 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1271 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1273 …2} "content" => Illuminate\Database\Eloquent\Collection {#1252 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1290 …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 => "*" ] } 6 => App\Models\Task {#1270 #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" => 1122208 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-20" "field_display_title" => "3.20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1288 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1287 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289 …2} "content" => Illuminate\Database\Eloquent\Collection {#1268 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1306 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122208 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-20" "field_display_title" => "3.20" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1269 …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 {#1288 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1287 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1289 …2} "content" => Illuminate\Database\Eloquent\Collection {#1268 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1306 …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 => "*" ] } 7 => App\Models\Task {#1286 #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" => 1122209 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-21" "field_display_title" => "3.21" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1285 …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 {#1304 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1303 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1305 …2} "content" => Illuminate\Database\Eloquent\Collection {#1284 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1322 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1122209 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-21" "field_display_title" => "3.21" "field_outside_task" => null …16 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 8 => App\Models\Task {#1302 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 9 => App\Models\Task {#1318 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 10 => App\Models\Task {#1334 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 11 => App\Models\Task {#1350 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1114155 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/page-49" "field_display_title" => "49" "field_folder" => "folder1" "field_image_name" => "49" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1072} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1012} "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 {#1096} "content" => Illuminate\Database\Eloquent\Collection {#1099} "next" => array:2 [ "refs" => "1114156" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114154" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1186} ] #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" => 1122204 "created_at" => "2026-04-08 17:28:58" "updated_at" => null "field_page_start" => "49" "field_page_end" => null "field_url" => "/7-klass/geometrija/shynybekov-uchebnik/3-16" "field_display_title" => "3.16" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1009} "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 {#1007} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1018} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1077} "content" => Illuminate\Database\Eloquent\Collection {#1010} "next" => array:2 [ "refs" => "1122205" "type" => "task" ] "previous" => array:2 [ "refs" => "1122203" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1068} "page" => array:2 [ "refs" => "1114155" "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 => "*" ] }
№3.16 (с. 49)
Условие rus. №3.16 (с. 49)
скриншот условия
3.16. Найдите внешний угол при третьей вершине треугольника, если два других угла равны:
1) $54^\circ$ и $36^\circ$;
2) $42^\circ$ и $78^\circ$;
3) $65^\circ$ и $35^\circ$;
4) $33^\circ$ и $120^\circ$.
Условие kz. №3.16 (с. 49)
Решение. №3.16 (с. 49)
Решение 2 rus. №3.16 (с. 49)
Для решения этой задачи используется свойство внешнего угла треугольника. Теорема о внешнем угле треугольника гласит, что внешний угол при любой вершине треугольника равен сумме двух внутренних углов, не смежных с ним.
Следовательно, для нахождения внешнего угла при третьей вершине нужно просто сложить два данных угла.
1) Даны углы $54^\circ$ и $36^\circ$.
Находим внешний угол при третьей вершине как сумму этих двух углов:
$54^\circ + 36^\circ = 90^\circ$.
Ответ: $90^\circ$.
2) Даны углы $42^\circ$ и $78^\circ$.
Находим внешний угол при третьей вершине как сумму этих двух углов:
$42^\circ + 78^\circ = 120^\circ$.
Ответ: $120^\circ$.
3) Даны углы $65^\circ$ и $35^\circ$.
Находим внешний угол при третьей вершине как сумму этих двух углов:
$65^\circ + 35^\circ = 100^\circ$.
Ответ: $100^\circ$.
4) Даны углы $33^\circ$ и $120^\circ$.
Находим внешний угол при третьей вершине как сумму этих двух углов:
$33^\circ + 120^\circ = 153^\circ$.
Ответ: $153^\circ$.
Другие задания:
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