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Номер 257, страница 79 - гдз по геометрии 7 класс учебник Мерзляк, Полонский
Авторы: Мерзляк А. Г., Полонский В. Б., Якир М. С.
Тип: Учебник
Издательство: Просвещение, Вентана-граф
Год издания: 2023 - 2026
Цвет обложки: оранжевый с графиком
ISBN: 978-5-09-105805-5
Популярные ГДЗ в 7 классе
Глава 2. Треугольники. Параграф 10. Признаки равнобедренного треугольника. Упражнения - номер 257, страница 79.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 599908 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_page_end" => null "field_url" => "/7-klass/geometrija/merzlyak-fgos/257" "field_display_title" => "257" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1078 #items: array:1 [ 0 => App\Models\Branch {#1034 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 599505 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "51" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ …50] #original: array:50 [ …50] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 599505 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "51" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075} ] #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 {#1199 #items: array:3 [ 0 => App\Models\Branch {#1209 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 599505 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Term {#1210 #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 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "51" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1248 #items: array:1 [ 0 => App\Models\Book {#1212 #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" => 904 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:2 [ 0 => App\Models\Term {#1211 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1215 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1216 #items: array:1 [ 0 => App\Models\Term {#1217 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1218 #items: array:2 [ 0 => App\Models\Term {#1219 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1220 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:3 [ 0 => App\Models\Term {#1222 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1223 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1224 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1225 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1226 #items: array:1 [ 0 => App\Models\Term {#1227 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:1 [ 0 => App\Models\Term {#1229 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Term {#1231 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1232 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1233 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1234 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:2 [ 0 => App\Models\Term {#1236 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1237 #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 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1238 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1239 #items: array:1 [ 0 => App\Models\Term {#1240 #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 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "с графиком" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1017" "field_priority" => "6" "field_default_folder" => "/geometrija_07/merzlyak-u23/" "field_isbn" => "978-5-09-105805-5" "field_cover" => array:1 [ 0 => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" "alt" => "" "width" => "2277" "height" => "3035" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1241 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1242 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1243 #items: [] #escapeWhenCastingToString: false } "field_url" => "/7-klass/geometrija/merzlyak-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:1 [ 0 => App\Models\Term {#1245 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2>Нужно ли изучать геометрию? </h2> <p> В седьмом классе учебные нагрузки возрастут. В расписании школьников появится такой предмет как геометрия. Поначалу новая наука вызывает искренний интерес, но уже через некоторое время ребята начинают испытывать трудности при ее освоении. Многие пытаются мотивировать нежелание делать уроки высказываниями вроде: «Да зачем она нужна?», «В жизни такое точно не пригодится», и т.д. Тем не менее оценки по предмету самым прямым образом влияют на общую успеваемость. С помощью «<strong>ГДЗ по Геометрии 7 класс Учебник Мерзляк, Полонский, Якир (Вентана-Граф)</strong>» можно разобраться в аспектах дисциплины и осознать ее смысл. </p> <p> Давайте рассмотрим, какие качества позволяет развить геометрия у учеников: <ol> <li>Логическое, образное мышление.</li> <li>Пространственное представление.</li> <li>Интуитивную и символическую умственную деятельность.</li> <li>Фантазию.</li> <li>Умение анализировать.</li> <li>Грамотную речь.</li> </ol> <p> Основное, что требуется от учащихся на уроках - внимательность. Иначе будет трудно понять, каким образом знание теорем поможет справиться с выполнением задач. Геометрия - наука сугубо практическая, поэтому учителя показывают наглядные примеры во время занятий. Но иногда у подростков все равно остаются вопросы, ответить на которые зачастую некому. Решебник позволит полноценно освоить новую тему и приобрести важные навыки. </p> <h2> Почему ученики выбирают ГДЗ к учебнику Мерзляка? </h2> <p> Учебники подчас содержат очень мало полезных сведений. Возникает ощущение, что авторы этих пособий сосредоточены только на написании разнообразных задач. Поэтому основную информацию по теории школьники получают от преподавателя. Но всегда могут возникнуть непредвиденные ситуации, например, ребенок заболел или не понял объяснения, даже просто отвлекся. Необходимо тщательно разобрать все упущенное, чтобы не потеряться потом в водовороте новых данных. Отличным помощником в этом деле станет <strong>сборник ответов по геометрии к учебнику Мерзляка за 7 класс</strong>. </p> <p> Подростки все чаще отдают предпочтение этому сборнику, так как: <ol> <li>в нем все понятно изложено;</li> <li>с его помощью выполнение домашних заданий отнимает всего несколько минут;</li> <li>можно исправить недочеты, до того как учитель увидит тетрадь;</li> <li>есть понятные наглядные примеры и подробные ответы, позволяющие сразу разобраться в сути вопроса.</li> </ol> <p> Заниматься с решебником можно в любое удобное время, так что учащиеся сами строят график работы, не зависят при этом от внешних условий. При этом есть постоянная возможность повторить ранее пройденные параграфы, что позволит хорошо подготовиться к контрольным и освежить память. Некоторые ребята заглядывают в пособие прямо на перемене, чем обеспечивают себе твердую пятерку на уроке. </p> <h2> Действительно ли онлайн-решебник помогает? </h2> <p> Многие взрослые беспокоятся, правда ли <strong>онлайн ответы по геометрии 7 класс к учебнику Мерзляка А. Г. (Вентана-Граф)</strong>» могут помочь детям или это просто очередная шпаргалка, которой они пользуются, лишь бы не учиться? Все зависит от подхода самих школьников. Естественно, есть ребята, которые начинают списывать с электронного пособия готовые решения. Правда, пользы это приносит мало, ведь учитель после первой же контрольной заметит, что ученик ничего не знает. </p> <p> Большинство же подростков: <ul> <li>изучают теорию в учебнике (если, конечно, она присутствует);</li> <li>самостоятельно выполняют домашнее задание;</li> <li>сверяют получившиеся ответы с теми, что даны в решебнике;</li> <li>у кого есть ошибки проводят их разбор и анализ.</li> </ul> <p> Учащиеся, которые подходят к использованию справочника ответственно, быстро добиваются хороших результатов, выбиваются в отличники и всегда уверены в том, что справятся с любыми поставленными задачами. </p>" "breadcrumbs" => array:3 [ "class" => 378 "subject" => 543 "class_subject" => 389 ] ] #original: array:50 [ "id" => 904 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1214} "field_class" => Illuminate\Database\Eloquent\Collection {#1216} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1218} "field_author" => Illuminate\Database\Eloquent\Collection {#1221} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1225} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1226} "field_country" => Illuminate\Database\Eloquent\Collection {#1228} "field_city" => Illuminate\Database\Eloquent\Collection {#1230} "field_series" => Illuminate\Database\Eloquent\Collection {#1232} "field_umk" => Illuminate\Database\Eloquent\Collection {#1233} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1234} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1235} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1238} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1239} "field_under_the_edition_degree" => null "field_cover_description" => "с графиком" "field_publication_year" => "2023" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1017" "field_priority" => "6" "field_default_folder" => "/geometrija_07/merzlyak-u23/" "field_isbn" => "978-5-09-105805-5" "field_cover" => array:1 [ 0 => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/geometrija_07/merzlyak-u23/covers/cover1.webp?ts=1738008352" "alt" => "" "width" => "2277" "height" => "3035" ] ] "field_popular_book" => null "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1241} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1242} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1243} "field_url" => "/7-klass/geometrija/merzlyak-fgos" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1244} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => "<!--Текст в низу страницы--> <h2>Нужно ли изучать геометрию? </h2> <p> В седьмом классе учебные нагрузки возрастут. В расписании школьников появится такой предмет как геометрия. Поначалу новая наука вызывает искренний интерес, но уже через некоторое время ребята начинают испытывать трудности при ее освоении. Многие пытаются мотивировать нежелание делать уроки высказываниями вроде: «Да зачем она нужна?», «В жизни такое точно не пригодится», и т.д. Тем не менее оценки по предмету самым прямым образом влияют на общую успеваемость. С помощью «<strong>ГДЗ по Геометрии 7 класс Учебник Мерзляк, Полонский, Якир (Вентана-Граф)</strong>» можно разобраться в аспектах дисциплины и осознать ее смысл. </p> <p> Давайте рассмотрим, какие качества позволяет развить геометрия у учеников: <ol> <li>Логическое, образное мышление.</li> <li>Пространственное представление.</li> <li>Интуитивную и символическую умственную деятельность.</li> <li>Фантазию.</li> <li>Умение анализировать.</li> <li>Грамотную речь.</li> </ol> <p> Основное, что требуется от учащихся на уроках - внимательность. Иначе будет трудно понять, каким образом знание теорем поможет справиться с выполнением задач. Геометрия - наука сугубо практическая, поэтому учителя показывают наглядные примеры во время занятий. Но иногда у подростков все равно остаются вопросы, ответить на которые зачастую некому. Решебник позволит полноценно освоить новую тему и приобрести важные навыки. </p> <h2> Почему ученики выбирают ГДЗ к учебнику Мерзляка? </h2> <p> Учебники подчас содержат очень мало полезных сведений. Возникает ощущение, что авторы этих пособий сосредоточены только на написании разнообразных задач. Поэтому основную информацию по теории школьники получают от преподавателя. Но всегда могут возникнуть непредвиденные ситуации, например, ребенок заболел или не понял объяснения, даже просто отвлекся. Необходимо тщательно разобрать все упущенное, чтобы не потеряться потом в водовороте новых данных. Отличным помощником в этом деле станет <strong>сборник ответов по геометрии к учебнику Мерзляка за 7 класс</strong>. </p> <p> Подростки все чаще отдают предпочтение этому сборнику, так как: <ol> <li>в нем все понятно изложено;</li> <li>с его помощью выполнение домашних заданий отнимает всего несколько минут;</li> <li>можно исправить недочеты, до того как учитель увидит тетрадь;</li> <li>есть понятные наглядные примеры и подробные ответы, позволяющие сразу разобраться в сути вопроса.</li> </ol> <p> Заниматься с решебником можно в любое удобное время, так что учащиеся сами строят график работы, не зависят при этом от внешних условий. При этом есть постоянная возможность повторить ранее пройденные параграфы, что позволит хорошо подготовиться к контрольным и освежить память. Некоторые ребята заглядывают в пособие прямо на перемене, чем обеспечивают себе твердую пятерку на уроке. </p> <h2> Действительно ли онлайн-решебник помогает? </h2> <p> Многие взрослые беспокоятся, правда ли <strong>онлайн ответы по геометрии 7 класс к учебнику Мерзляка А. Г. (Вентана-Граф)</strong>» могут помочь детям или это просто очередная шпаргалка, которой они пользуются, лишь бы не учиться? Все зависит от подхода самих школьников. Естественно, есть ребята, которые начинают списывать с электронного пособия готовые решения. Правда, пользы это приносит мало, ведь учитель после первой же контрольной заметит, что ученик ничего не знает. </p> <p> Большинство же подростков: <ul> <li>изучают теорию в учебнике (если, конечно, она присутствует);</li> <li>самостоятельно выполняют домашнее задание;</li> <li>сверяют получившиеся ответы с теми, что даны в решебнике;</li> <li>у кого есть ошибки проводят их разбор и анализ.</li> </ul> <p> Учащиеся, которые подходят к использованию справочника ответственно, быстро добиваются хороших результатов, выбиваются в отличники и всегда уверены в том, что справятся с любыми поставленными задачами. </p>" "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 {#1246 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 599505 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Треугольники" "field_branch_order" => "2" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213} "field_page_start" => "51" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1248} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1246} ] #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 {#1247 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 599515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Признаки равнобедренного треугольника" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1252 #items: array:1 [ 0 => App\Models\Term {#1249 #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 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_page_start" => "76" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1251 #items: array:1 [ 0 => App\Models\Book {#1212} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1250 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 599515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Признаки равнобедренного треугольника" "field_branch_order" => "10" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1252} "field_page_start" => "76" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1251} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1250} ] #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\Branch {#1253 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 599517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1254 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "79" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:1 [ 0 => App\Models\Book {#1212} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1264 #items: array:1 [ 0 => App\Models\Branch {#1263 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …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:24 [ "id" => 599517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1254} "field_page_start" => "79" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1255} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1264} ] #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 {#1188 #items: array:10 [ 0 => App\Models\Element {#1169 #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" => 744349 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Edition {#1171 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "text" => "<p><strong>257.</strong> Серединный перпендикуляр стороны AC треугольника ABC проходит через вершину B. Найдите $\angle C$, если $\angle A = 17^\circ$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "1640" "height" => 180 "path" => "/media/geometrija_07/merzlyak-u23/0-00/257-1.webp?ts=1738080370" ] ] ] #original: array:7 [ "id" => 744349 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "text" => "<p><strong>257.</strong> Серединный перпендикуляр стороны AC треугольника ABC проходит через вершину B. Найдите $\angle C$, если $\angle A = 17^\circ$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "1640" "height" => 180 "path" => "/media/geometrija_07/merzlyak-u23/0-00/257-1.webp?ts=1738080370" ] ] ] #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 {#1149 #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" => 749283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Edition {#1148 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "694" "height" => 2015 "path" => "/media/geometrija_07/merzlyak-u23/2-00/257-1.webp?ts=1738085036" ] ] ] #original: array:6 [ "id" => 749283 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1139} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "694" "height" => 2015 "path" => "/media/geometrija_07/merzlyak-u23/2-00/257-1.webp?ts=1738085036" ] ] ] #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 {#1141 #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" => 749956 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Edition {#1140 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "1400" "height" => 728 "path" => "/media/geometrija_07/merzlyak-u23/3-00/257-1.webp?ts=1738085774" ] ] ] #original: array:6 [ "id" => 749956 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1128} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "1400" "height" => 728 "path" => "/media/geometrija_07/merzlyak-u23/3-00/257-1.webp?ts=1738085774" ] ] ] #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 {#1118 #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" => 752361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1110 #items: array:1 [ 0 => App\Models\Edition {#1117 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "600" "height" => 274 "path" => "/media/geometrija_07/merzlyak-u23/4-00/257-1.webp?ts=1738089755" ] ] ] #original: array:6 [ "id" => 752361 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1110} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "600" "height" => 274 "path" => "/media/geometrija_07/merzlyak-u23/4-00/257-1.webp?ts=1738089755" ] ] ] #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\Element {#1134 #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" => 750945 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1124 #items: array:1 [ 0 => App\Models\Edition {#1132 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "760" "height" => 1200 "path" => "/media/geometrija_07/merzlyak-u23/5-00/257-1.webp?ts=1738086613" ] ] ] #original: array:6 [ "id" => 750945 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1124} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "760" "height" => 1200 "path" => "/media/geometrija_07/merzlyak-u23/5-00/257-1.webp?ts=1738086613" ] ] ] #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\Element {#1095 #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" => 1441410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Edition {#1096 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "text" => "<p><strong>Решение:</strong></p><p>Пусть дан треугольник $ABC$. По условию, серединный перпендикуляр к стороне $AC$ проходит через вершину $B$.</p><p>Серединный перпендикуляр к отрезку – это прямая, все точки которой равноудалены от концов этого отрезка. Поскольку вершина $B$ лежит на серединном перпендикуляре к стороне $AC$, расстояние от точки $B$ до точки $A$ равно расстоянию от точки $B$ до точки $C$.</p><p>Таким образом, мы имеем равенство сторон:</p><p>$AB = BC$</p><p>Треугольник, у которого две стороны равны, является равнобедренным. Следовательно, треугольник $ABC$ – равнобедренный с основанием $AC$.</p><p>В равнобедренном треугольнике углы при основании равны. В данном случае это углы $\angle A$ и $\angle C$.</p><p>$\angle C = \angle A$</p><p>Из условия задачи известно, что $\angle A = 17^{\circ}$. Следовательно,</p><p>$\angle C = 17^{\circ}$</p><p><strong>Ответ:</strong> $17^{\circ}$.</p>" ] #original: array:6 [ "id" => 1441410 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1085} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "text" => "<p><strong>Решение:</strong></p><p>Пусть дан треугольник $ABC$. По условию, серединный перпендикуляр к стороне $AC$ проходит через вершину $B$.</p><p>Серединный перпендикуляр к отрезку – это прямая, все точки которой равноудалены от концов этого отрезка. Поскольку вершина $B$ лежит на серединном перпендикуляре к стороне $AC$, расстояние от точки $B$ до точки $A$ равно расстоянию от точки $B$ до точки $C$.</p><p>Таким образом, мы имеем равенство сторон:</p><p>$AB = BC$</p><p>Треугольник, у которого две стороны равны, является равнобедренным. Следовательно, треугольник $ABC$ – равнобедренный с основанием $AC$.</p><p>В равнобедренном треугольнике углы при основании равны. В данном случае это углы $\angle A$ и $\angle C$.</p><p>$\angle C = \angle A$</p><p>Из условия задачи известно, что $\angle A = 17^{\circ}$. Следовательно,</p><p>$\angle C = 17^{\circ}$</p><p><strong>Ответ:</strong> $17^{\circ}$.</p>" ] #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\Element {#1165 #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" => 747932 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Edition {#1160 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "text" => "<p><strong>257.</strong> На рисунке 184 $AB = CD, AC = BD$. Докажите, что $\triangle BOC$ – равнобедренный.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "1058" "height" => 159 "path" => "/media/geometrija_07/merzlyak-u23/old0-00/257-1.webp?ts=1738081376" ] ] ] #original: array:7 [ "id" => 747932 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1146} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "text" => "<p><strong>257.</strong> На рисунке 184 $AB = CD, AC = BD$. Докажите, что $\triangle BOC$ – равнобедренный.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "1058" "height" => 159 "path" => "/media/geometrija_07/merzlyak-u23/old0-00/257-1.webp?ts=1738081376" ] ] ] #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\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" => 751688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1076 #items: array:1 [ 0 => App\Models\Edition {#1123 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "694" "height" => 1611 "path" => "/media/geometrija_07/merzlyak-u23/old2-00/257-1.webp?ts=1738089121" ] ] ] #original: array:6 [ "id" => 751688 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1076} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "694" "height" => 1611 "path" => "/media/geometrija_07/merzlyak-u23/old2-00/257-1.webp?ts=1738089121" ] ] ] #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\Element {#1112 #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" => 753050 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102 #items: array:1 [ 0 => App\Models\Edition {#1111 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "1400" "height" => 839 "path" => "/media/geometrija_07/merzlyak-u23/old3-00/257-1.webp?ts=1738091611" ] ] ] #original: array:6 [ "id" => 753050 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1102} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:1 [ 0 => array:5 [ "name" => "257-1.png" "alt" => null "width" => "1400" "height" => 839 "path" => "/media/geometrija_07/merzlyak-u23/old3-00/257-1.webp?ts=1738091611" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 9 => App\Models\Element {#1105 #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" => 753983 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094 #items: array:1 [ 0 => App\Models\Edition {#1103 #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 [ …21] #original: array:21 [ …21] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "600" "height" => 157 "path" => "/media/geometrija_07/merzlyak-u23/old4-00/257-1.webp?ts=1738092559" ] 1 => array:5 [ "name" => "257-2.jpg" "alt" => null "width" => "600" "height" => 165 "path" => "/media/geometrija_07/merzlyak-u23/old4-00/257-2.webp?ts=1738092559" ] ] ] #original: array:6 [ "id" => 753983 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1094} "task" => array:2 [ "refs" => "599908" "type" => "task" ] "img" => array:2 [ 0 => array:5 [ "name" => "257-1.jpg" "alt" => null "width" => "600" "height" => 157 "path" => "/media/geometrija_07/merzlyak-u23/old4-00/257-1.webp?ts=1738092559" ] 1 => array:5 [ "name" => "257-2.jpg" "alt" => null "width" => "600" "height" => 165 "path" => "/media/geometrija_07/merzlyak-u23/old4-00/257-2.webp?ts=1738092559" ] ] ] #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" => "599909" "type" => "task" ] "previous" => array:2 [ "refs" => "599907" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1174 #items: array:1 [ 0 => App\Models\Book {#1212} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1194 #items: array:1 [ 0 => App\Models\BookPage {#1192 #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" => 964903 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_url" => "/7-klass/geometrija/merzlyak-fgos/page-79" "field_display_title" => "79" "field_folder" => "1" "field_image_name" => "79" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1193 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Book {#1212} ] #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 {#1153 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:2 [ 0 => App\Models\Element {#1176 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Element {#1177 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "964904" "type" => "book_page" ] "previous" => array:2 [ "refs" => "964902" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1704 #items: array:10 [ 0 => App\Models\Task {#1720 #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] } 1 => App\Models\Task {#1733 #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] } 2 => App\Models\Task {#1737 #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] } 3 => App\Models\Task {#1731 #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 …4 } 4 => App\Models\Task {#1742 …30} 5 => App\Models\Task {#1744 …30} 6 => App\Models\Task {#1754 …30} 7 => App\Models\Task {#1854 …30} 8 => App\Models\Task {#1882 …30} 9 => App\Models\Task {#1911 …30} ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 964903 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_url" => "/7-klass/geometrija/merzlyak-fgos/page-79" "field_display_title" => "79" "field_folder" => "1" "field_image_name" => "79" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1193} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1206} "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 {#1153} "content" => Illuminate\Database\Eloquent\Collection {#1162} "next" => array:2 [ "refs" => "964904" "type" => "book_page" ] "previous" => array:2 [ "refs" => "964902" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1704} ] #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" => 599908 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "79" "field_page_end" => null "field_url" => "/7-klass/geometrija/merzlyak-fgos/257" "field_display_title" => "257" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1078} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1199} "content" => Illuminate\Database\Eloquent\Collection {#1188} "next" => array:2 [ "refs" => "599909" "type" => "task" ] "previous" => array:2 [ "refs" => "599907" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1174} "page" => array:2 [ "refs" => "964903" "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 => "*" ] }
№257 (с. 79)
Условие 2023. №257 (с. 79)
скриншот условия
257. Серединный перпендикуляр стороны AC треугольника ABC проходит через вершину B. Найдите $\angle C$, если $\angle A = 17^\circ$.
Решение 2 (2023). №257 (с. 79)
Решение 3 (2023). №257 (с. 79)
Решение 4 (2023). №257 (с. 79)
Решение 5 (2023). №257 (с. 79)
Решение 6 (2023). №257 (с. 79)
Решение:
Пусть дан треугольник $ABC$. По условию, серединный перпендикуляр к стороне $AC$ проходит через вершину $B$.
Серединный перпендикуляр к отрезку – это прямая, все точки которой равноудалены от концов этого отрезка. Поскольку вершина $B$ лежит на серединном перпендикуляре к стороне $AC$, расстояние от точки $B$ до точки $A$ равно расстоянию от точки $B$ до точки $C$.
Таким образом, мы имеем равенство сторон:
$AB = BC$
Треугольник, у которого две стороны равны, является равнобедренным. Следовательно, треугольник $ABC$ – равнобедренный с основанием $AC$.
В равнобедренном треугольнике углы при основании равны. В данном случае это углы $\angle A$ и $\angle C$.
$\angle C = \angle A$
Из условия задачи известно, что $\angle A = 17^{\circ}$. Следовательно,
$\angle C = 17^{\circ}$
Ответ: $17^{\circ}$.
Условие (2015-2022). №257 (с. 79)
скриншот условия
257. На рисунке 184 $AB = CD, AC = BD$. Докажите, что $\triangle BOC$ – равнобедренный.
Решение 2 (2015-2022). №257 (с. 79)
Решение 3 (2015-2022). №257 (с. 79)
Решение 4 (2015-2022). №257 (с. 79)
Другие задания:
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