Предмет: Геометрия, автор: Boomer111

Допоможіть будласка!

У Δ ABCD діагональ BD дорівнює 13 см. позначено точки M, N, K, L - середини його сторін. Знайти периметр чотитируктика M, N, K, L користуючись такими геометричними твердженнями:

Властивости прямокутника;

Означення середньої лінії трикутника;

Властивості середньої лінії трикутника;

Приложения:

Ответы

Автор ответа: cos20093

Из рисунка понятно, что ABCD прямоугольник (из условия это совершенно не понятно).

У прямоугольника диагонали равны. Поэтому AC = BD = 13;

Далее, MN = KL = BD/2; ML = KN = AC/2; (ну, например, MN - средняя линяя треугольника BDC, поэтому MN II BD и MN = BD/2; остальные отрезки находятся аналогично).

Поэтому MNKL - ромб со стороной BD/2 = 6,5; его периметр равен 26.

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