Parallelogram ABCD: Comparing Triangles Formed by Diagonal AD

Question

Look at the parallelogram ABCD below.

What can be said about triangles ACD and ABD?

00:00 What can be said about triangles ACD and ABD

00:03 The quadrilateral is a parallelogram according to the given

00:06 Opposite sides are equal in a parallelogram (S)

00:21 Opposite angles are equal in a parallelogram (A)

00:29 The triangles are congruent according to SAS theorem

00:49 Congruent triangles have equal areas

01:01 Congruent triangles have equal perimeters

01:19 Congruent triangles are necessarily similar

01:23 And this is the solution to the question

According to the side-angle-side theorem, the triangles are similar and coincide with each other:

AC = BD (Any pair of opposite sides of a parallelogram are equal)

Angle C is equal to angle B.

AB = CD (Any pair of opposite sides of the parallelogram are equal)

Therefore, all of the answers are correct.

All answers are correct.