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Номер 3.9, страница 17 - 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 1. Начальные геометрические сведения. Параграф 3. Измерение длин отрезков - номер 3.9, страница 17.
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" => 1129433 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-9" "field_display_title" => "3.9" "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" => "2026-04-10 00:54:11" "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 00:54:11" "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 {#1043 #items: array:1 [ 0 => App\Models\Branch {#1006 #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" => 1129359 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Начальные геометрические сведения" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1011 #items: array:1 [ 0 => App\Models\Term {#1010 #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 00:54:11" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Глава" "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" => "5" "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 {#1012 #items: array:1 [ 0 => App\Models\Book {#1013 #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 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1014 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1016 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1018 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1020 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1023 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1024 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1026 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1028 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1030 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1031 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1032 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1033 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1035 …2} "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 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1037 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 2907 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1014 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1016 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1018 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1020 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1023 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1024 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1026 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1028 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1030 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1031 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1032 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1033 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1035 …2} "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 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1036 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1037 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1038 …2} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1040 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1129359 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Начальные геометрические сведения" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1011} "field_page_start" => "5" "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 {#1012} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1040} ] #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 {#1076 #items: array:2 [ 0 => App\Models\Branch {#1084 #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" => 1129359 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Начальные геометрические сведения" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1085 #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 00:54:11" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Глава" "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" => "5" "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 {#1116 #items: array:1 [ 0 => App\Models\Book {#1087 #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 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1089 #items: array:1 [ 0 => App\Models\Term {#1086 #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 00:54:11" "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" => "2026-04-10 00:54:11" "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 {#1090 #items: array:1 [ 0 => App\Models\Term {#1091 #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 00:54:11" "updated_at" => null "name" => "7" "field_cases" => array:6 [ …6] "field_translit" => "sedmoj" ] #original: array:6 [ "id" => 5456 "created_at" => "2026-04-10 00:54:11" "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 {#1092 #items: array:1 [ 0 => App\Models\Term {#1093 #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 00:54:11" "updated_at" => null "name" => "Мектеп" "field_cases" => array:6 [ …6] "field_translit" => "mektep" ] #original: array:6 [ "id" => 6996 "created_at" => "2026-04-10 00:54:11" "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 {#1094 #items: array:2 [ 0 => App\Models\Term {#1095 #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 00:54:11" "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 00:54:11" "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 {#1096 #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 00:54:11" "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 00:54:11" "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 {#1097 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Term {#1099 #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 00:54:11" "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 00:54:11" "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 {#1100 #items: array:1 [ 0 => App\Models\Term {#1101 #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 00:54:11" "updated_at" => null "name" => "Казахстан" "field_cases" => array:6 [ …6] "field_translit" => "kazakhstan" ] #original: array:6 [ "id" => 6994 "created_at" => "2026-04-10 00:54:11" "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 {#1102 #items: array:1 [ 0 => App\Models\Term {#1103 #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 00:54:11" "updated_at" => null "name" => "Алматы" "field_cases" => array:6 [ …6] "field_translit" => "almaty" ] #original: array:6 [ "id" => 6995 "created_at" => "2026-04-10 00:54:11" "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 {#1104 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1105 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1106 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1107 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1109 #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" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1110 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1111 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1112 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1113 #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 00:54:11" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1089} "field_class" => Illuminate\Database\Eloquent\Collection {#1090} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1092} "field_author" => Illuminate\Database\Eloquent\Collection {#1094} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1097} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1098} "field_country" => Illuminate\Database\Eloquent\Collection {#1100} "field_city" => Illuminate\Database\Eloquent\Collection {#1102} "field_series" => Illuminate\Database\Eloquent\Collection {#1104} "field_umk" => Illuminate\Database\Eloquent\Collection {#1105} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1106} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1107} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1108} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1109} "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" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/Smirnova-u17/covers/cover1.webp" "alt" => "" "width" => "1632" "height" => "2472" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1110} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1111} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1112} "field_url" => "/7-klass/geometrija/smirnova-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1113} "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 {#1114 #items: [] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1129359 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Начальные геометрические сведения" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1088} "field_page_start" => "5" "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 {#1116} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1114} ] #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 {#1115 #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" => 1129362 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Измерение длин отрезков" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1120 #items: array:1 [ 0 => App\Models\Term {#1117 #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 00:54:11" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "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" => "15" "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 {#1119 #items: array:1 [ 0 => App\Models\Book {#1087} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Branch {#1006} ] #escapeWhenCastingToString: false } ] #original: array:23 [ "id" => 1129362 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_display_title" => "Измерение длин отрезков" "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1120} "field_page_start" => "15" "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 {#1119} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1118} ] #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 {#1073 #items: array:3 [ 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" => 1319509 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1058 #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" => 5009 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1063 …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" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5009 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1063 …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" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1059 …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" => "1129433" "type" => "task" ] "text" => "<p><strong>3.9.</strong> Точки $A$, $B$, $C$ принадлежат одной прямой. Принадлежит ли точка $B$ отрезку $AC$, если $AC = 3 \text{ см}$, $BC = 5 \text{ см}$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1710" "height" => 188 "path" => "/media/geometrija_07/Smirnova-u17/0-03/9-1.webp?ts=1753982202" ] ] ] #original: array:7 [ "id" => 1319509 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1058} "task" => array:2 [ "refs" => "1129433" "type" => "task" ] "text" => "<p><strong>3.9.</strong> Точки $A$, $B$, $C$ принадлежат одной прямой. Принадлежит ли точка $B$ отрезку $AC$, если $AC = 3 \text{ см}$, $BC = 5 \text{ см}$?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1710" "height" => 188 "path" => "/media/geometrija_07/Smirnova-u17/0-03/9-1.webp?ts=1753982202" ] ] ] #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 {#1060 #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" => 1319890 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Edition {#1057 #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 00:54:11" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053 …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 {#1055 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5010 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053 …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 {#1055 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_process_formula" => "" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1051 …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" => "1129433" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1075" "height" => 351 "path" => "/media/geometrija_07/Smirnova-u17/1-03/9-1.webp?ts=1753982308" ] 1 => array:5 [ "name" => "9-2.jpg" "alt" => null "width" => "1347" "height" => 710 "path" => "/media/geometrija_07/Smirnova-u17/1-03/9-2.webp?ts=1753982308" ] ] ] #original: array:6 [ "id" => 1319890 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1050} "task" => array:2 [ "refs" => "1129433" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1075" "height" => 351 "path" => "/media/geometrija_07/Smirnova-u17/1-03/9-1.webp?ts=1753982308" ] 1 => array:5 [ "name" => "9-2.jpg" "alt" => null "width" => "1347" "height" => 710 "path" => "/media/geometrija_07/Smirnova-u17/1-03/9-2.webp?ts=1753982308" ] ] ] #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 {#1052 #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" => 1541299 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Edition {#1049 #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 00:54:11" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …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 {#1044 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1075 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5631 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "title" => "Решение 2" "field_order" => "3" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1048 …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 {#1044 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_process_formula" => "katex" "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" => "1129433" "type" => "task" ] "text" => "<p>Чтобы точка $B$ принадлежала отрезку $AC$, необходимо, чтобы она лежала между точками $A$ и $C$. В этом случае, согласно аксиоме измерения отрезков, длина всего отрезка $AC$ должна быть равна сумме длин его частей, отрезков $AB$ и $BC$. Это выражается формулой:</p><p>$AB + BC = AC$</p><p>Из условия задачи нам даны следующие длины:</p><p>$AC = 3$ см</p><p>$BC = 5$ см</p><p>Давайте проверим, может ли выполняться равенство. Если бы точка $B$ лежала на отрезке $AC$, то длина отрезка $BC$ (как части) не могла бы быть больше длины всего отрезка $AC$. Однако, мы видим, что $5 \text{ см} > 3 \text{ см}$, то есть $BC > AC$.</p><p>Это противоречие означает, что точка $B$ не может находиться на отрезке $AC$.</p><p>Поскольку точки $A$, $B$, $C$ лежат на одной прямой, возможны другие варианты их взаимного расположения. Рассмотрим их:</p><p><strong>1.</strong> <strong>Точка C лежит между точками A и B.</strong><br>В этом случае выполняется равенство $AC + CB = AB$. Подставляя известные значения, получаем: $AB = 3 \text{ см} + 5 \text{ см} = 8 \text{ см}$. Такое расположение возможно.<br><svg width="210" height="40" xmlns="http://www.w3.org/2000/svg"><line x1="10" y1="20" x2="190" y2="20" stroke="black" stroke-width="1.5"></line><circle cx="10" cy="20" r="3" fill="black"></circle><text x="5" y="12" font-size="14">A</text><circle cx="78" cy="20" r="3" fill="black"></circle><text x="73" y="12" font-size="14">C</text><circle cx="190" cy="20" r="3" fill="black"></circle><text x="185" y="12" font-size="14">B</text></svg></p><p><strong>2.</strong> <strong>Точка A лежит между точками B и C.</strong><br>В этом случае выполняется равенство $BA + AC = BC$. Отсюда можно найти длину отрезка $BA$: $BA = BC - AC = 5 \text{ см} - 3 \text{ см} = 2 \text{ см}$. Такое расположение также возможно.<br><svg width="210" height="40" xmlns="http://www.w3.org/2000/svg"><line x1="10" y1="20" x2="190" y2="20" stroke="black" stroke-width="1.5"></line><circle cx="10" cy="20" r="3" fill="black"></circle><text x="5" y="12" font-size="14">B</text><circle cx="82" cy="20" r="3" fill="black"></circle><text x="77" y="12" font-size="14">A</text><circle cx="190" cy="20" r="3" fill="black"></circle><text x="185" y="12" font-size="14">C</text></svg></p><p>В обоих допустимых случаях расположения точек на прямой точка $B$ не принадлежит отрезку $AC$.</p><p><strong>Ответ:</strong> Нет, точка B не принадлежит отрезку AC, так как длина отрезка $BC$ больше длины отрезка $AC$.</p>" ] #original: array:6 [ "id" => 1541299 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1079} "task" => array:2 [ "refs" => "1129433" "type" => "task" ] "text" => "<p>Чтобы точка $B$ принадлежала отрезку $AC$, необходимо, чтобы она лежала между точками $A$ и $C$. В этом случае, согласно аксиоме измерения отрезков, длина всего отрезка $AC$ должна быть равна сумме длин его частей, отрезков $AB$ и $BC$. Это выражается формулой:</p><p>$AB + BC = AC$</p><p>Из условия задачи нам даны следующие длины:</p><p>$AC = 3$ см</p><p>$BC = 5$ см</p><p>Давайте проверим, может ли выполняться равенство. Если бы точка $B$ лежала на отрезке $AC$, то длина отрезка $BC$ (как части) не могла бы быть больше длины всего отрезка $AC$. Однако, мы видим, что $5 \text{ см} > 3 \text{ см}$, то есть $BC > AC$.</p><p>Это противоречие означает, что точка $B$ не может находиться на отрезке $AC$.</p><p>Поскольку точки $A$, $B$, $C$ лежат на одной прямой, возможны другие варианты их взаимного расположения. Рассмотрим их:</p><p><strong>1.</strong> <strong>Точка C лежит между точками A и B.</strong><br>В этом случае выполняется равенство $AC + CB = AB$. Подставляя известные значения, получаем: $AB = 3 \text{ см} + 5 \text{ см} = 8 \text{ см}$. Такое расположение возможно.<br><svg width="210" height="40" xmlns="http://www.w3.org/2000/svg"><line x1="10" y1="20" x2="190" y2="20" stroke="black" stroke-width="1.5"></line><circle cx="10" cy="20" r="3" fill="black"></circle><text x="5" y="12" font-size="14">A</text><circle cx="78" cy="20" r="3" fill="black"></circle><text x="73" y="12" font-size="14">C</text><circle cx="190" cy="20" r="3" fill="black"></circle><text x="185" y="12" font-size="14">B</text></svg></p><p><strong>2.</strong> <strong>Точка A лежит между точками B и C.</strong><br>В этом случае выполняется равенство $BA + AC = BC$. Отсюда можно найти длину отрезка $BA$: $BA = BC - AC = 5 \text{ см} - 3 \text{ см} = 2 \text{ см}$. Такое расположение также возможно.<br><svg width="210" height="40" xmlns="http://www.w3.org/2000/svg"><line x1="10" y1="20" x2="190" y2="20" stroke="black" stroke-width="1.5"></line><circle cx="10" cy="20" r="3" fill="black"></circle><text x="5" y="12" font-size="14">B</text><circle cx="82" cy="20" r="3" fill="black"></circle><text x="77" y="12" font-size="14">A</text><circle cx="190" cy="20" r="3" fill="black"></circle><text x="185" y="12" font-size="14">C</text></svg></p><p>В обоих допустимых случаях расположения точек на прямой точка $B$ не принадлежит отрезку $AC$.</p><p><strong>Ответ:</strong> Нет, точка B не принадлежит отрезку AC, так как длина отрезка $BC$ больше длины отрезка $AC$.</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" => "1129434" "type" => "task" ] "previous" => array:2 [ "refs" => "1129432" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Book {#1087} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\BookPage {#1045 #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" => 1114334 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-17" "field_display_title" => "17" "field_folder" => "1" "field_image_name" => "17" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1046 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Book {#1087} ] #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 {#1083 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Element {#1126 #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" => 1290521 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1290521 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 …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" => "1114335" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114333" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:10 [ 0 => App\Models\Task {#1241 #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" => 1129424 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/vopr-3" "field_display_title" => "Вопросы" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1242 …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 {#1243 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245 …2} "content" => Illuminate\Database\Eloquent\Collection {#1248 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1254 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129424 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/vopr-3" "field_display_title" => "Вопросы" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1242 …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 {#1243 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1244 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1245 …2} "content" => Illuminate\Database\Eloquent\Collection {#1248 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1254 …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 {#1247 #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" => 1129425 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-1" "field_display_title" => "3.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 …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 {#1253 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1251 …2} "content" => Illuminate\Database\Eloquent\Collection {#1250 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1268 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129425 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-1" "field_display_title" => "3.1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 …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 {#1253 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1255 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1251 …2} "content" => Illuminate\Database\Eloquent\Collection {#1250 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1268 …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 {#1252 #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" => 1129426 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-2" "field_display_title" => "3.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 …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 {#1267 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1269 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265 …2} "content" => Illuminate\Database\Eloquent\Collection {#1264 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1282 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129426 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-2" "field_display_title" => "3.2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249 …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 {#1267 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1269 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1265 …2} "content" => Illuminate\Database\Eloquent\Collection {#1264 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1282 …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 {#1266 #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" => 1129427 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-3" "field_display_title" => "3.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 …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 {#1281 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1283 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1279 …2} "content" => Illuminate\Database\Eloquent\Collection {#1278 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1296 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129427 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-3" "field_display_title" => "3.3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1263 …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 {#1281 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1283 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1279 …2} "content" => Illuminate\Database\Eloquent\Collection {#1278 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1296 …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 {#1280 #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" => 1129428 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-4" "field_display_title" => "3.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1277 …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 {#1295 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1297 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 …2} "content" => Illuminate\Database\Eloquent\Collection {#1292 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1310 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129428 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-4" "field_display_title" => "3.4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1277 …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 {#1295 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1297 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1293 …2} "content" => Illuminate\Database\Eloquent\Collection {#1292 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1310 …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 {#1294 #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" => 1129429 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-5" "field_display_title" => "3.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1291 …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 {#1309 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1311 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1307 …2} "content" => Illuminate\Database\Eloquent\Collection {#1306 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1324 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129429 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-5" "field_display_title" => "3.5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1291 …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 {#1309 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1311 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1307 …2} "content" => Illuminate\Database\Eloquent\Collection {#1306 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1324 …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 {#1308 #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" => 1129430 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-6" "field_display_title" => "3.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1305 …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 {#1323 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1325 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1321 …2} "content" => Illuminate\Database\Eloquent\Collection {#1320 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1338 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129430 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-6" "field_display_title" => "3.6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1305 …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 {#1323 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1325 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1321 …2} "content" => Illuminate\Database\Eloquent\Collection {#1320 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1338 …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 {#1322 #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" => 1129431 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-7" "field_display_title" => "3.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1319 …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 {#1337 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1339 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1335 …2} "content" => Illuminate\Database\Eloquent\Collection {#1334 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1352 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1129431 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-7" "field_display_title" => "3.7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1319 …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 {#1337 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1339 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1335 …2} "content" => Illuminate\Database\Eloquent\Collection {#1334 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1352 …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 => "*" ] } 8 => App\Models\Task {#1336 #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" => 1129432 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-8" "field_display_title" => "3.8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1333 …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 {#1351 …2} …7 ] #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 {#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" => 1114334 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_url" => "/7-klass/geometrija/smirnova-uchebnik/page-17" "field_display_title" => "17" "field_folder" => "1" "field_image_name" => "17" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1046} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1074} "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 {#1083} "content" => Illuminate\Database\Eloquent\Collection {#1127} "next" => array:2 [ "refs" => "1114335" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1114333" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1225} ] #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" => 1129433 "created_at" => "2026-04-10 00:54:11" "updated_at" => null "field_page_start" => "17" "field_page_end" => null "field_url" => "/7-klass/geometrija/smirnova-uchebnik/03-9" "field_display_title" => "3.9" "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 {#1043} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1076} "content" => Illuminate\Database\Eloquent\Collection {#1073} "next" => array:2 [ "refs" => "1129434" "type" => "task" ] "previous" => array:2 [ "refs" => "1129432" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1069} "page" => array:2 [ "refs" => "1114334" "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 => "*" ] }
№3.9 (с. 17)
Условие. №3.9 (с. 17)
скриншот условия
3.9. Точки $A$, $B$, $C$ принадлежат одной прямой. Принадлежит ли точка $B$ отрезку $AC$, если $AC = 3 \text{ см}$, $BC = 5 \text{ см}$?
Решение. №3.9 (с. 17)
Решение 2. №3.9 (с. 17)
Чтобы точка $B$ принадлежала отрезку $AC$, необходимо, чтобы она лежала между точками $A$ и $C$. В этом случае, согласно аксиоме измерения отрезков, длина всего отрезка $AC$ должна быть равна сумме длин его частей, отрезков $AB$ и $BC$. Это выражается формулой:
$AB + BC = AC$
Из условия задачи нам даны следующие длины:
$AC = 3$ см
$BC = 5$ см
Давайте проверим, может ли выполняться равенство. Если бы точка $B$ лежала на отрезке $AC$, то длина отрезка $BC$ (как части) не могла бы быть больше длины всего отрезка $AC$. Однако, мы видим, что $5 \text{ см} > 3 \text{ см}$, то есть $BC > AC$.
Это противоречие означает, что точка $B$ не может находиться на отрезке $AC$.
Поскольку точки $A$, $B$, $C$ лежат на одной прямой, возможны другие варианты их взаимного расположения. Рассмотрим их:
1. Точка C лежит между точками A и B.
В этом случае выполняется равенство $AC + CB = AB$. Подставляя известные значения, получаем: $AB = 3 \text{ см} + 5 \text{ см} = 8 \text{ см}$. Такое расположение возможно.
2. Точка A лежит между точками B и C.
В этом случае выполняется равенство $BA + AC = BC$. Отсюда можно найти длину отрезка $BA$: $BA = BC - AC = 5 \text{ см} - 3 \text{ см} = 2 \text{ см}$. Такое расположение также возможно.
В обоих допустимых случаях расположения точек на прямой точка $B$ не принадлежит отрезку $AC$.
Ответ: Нет, точка B не принадлежит отрезку AC, так как длина отрезка $BC$ больше длины отрезка $AC$.
Другие задания:
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