Question

В прямоугольнике ABCDпроведена диагональ BD. Докажите что треугольник ABD и BCD равны Помогите пожалуйста

Answer 1

1)ВС\\АД при секущей ВД(т.к прямоугольник)
углы накрест лежащие СВД=ВДА,АВД=ВДС
Вд-общая сторона,следовательно треугольники равные по стороне и 2 прилежащим к ней углам.

Answer 2

Proof that triangles ABD and BCD are congruent

To prove that triangles ABD and BCD are congruent, we can use the Side-Angle-Side (SAS) congruence criterion. According to this criterion, if two triangles have two sides and the included angle of one triangle equal to the corresponding two sides and included angle of the other triangle, then the triangles are congruent.

In this case, we have the following information: - Triangle ABD: Side AB is equal to side BC (since they are opposite sides of the rectangle), side AD is equal to side CD (since they are opposite sides of the rectangle), and angle ABD is equal to angle CBD (since they are vertical angles). - Triangle BCD: Side BC is equal to side AB (since they are opposite sides of the rectangle), side CD is equal to side AD (since they are opposite sides of the rectangle), and angle CBD is equal to angle ABD (since they are vertical angles).

Therefore, we have two sides and the included angle of triangle ABD equal to the corresponding two sides and included angle of triangle BCD. By the SAS congruence criterion, we can conclude that triangles ABD and BCD are congruent.

Note: The search results did not provide a direct proof for the congruence of triangles ABD and BCD. However, the given information about the rectangle and the properties of vertical angles can be used to establish the congruence.