Parallelogram ABCD: Comparing Triangles Formed by Diagonal AD

Look at the parallelogram ABCD below.

AAABBBDDDCCC

What can be said about triangles ACD and ABD?

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Step-by-step video solution

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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

Step-by-step written solution

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1

Understand the problem

Look at the parallelogram ABCD below.

AAABBBDDDCCC

What can be said about triangles ACD and ABD?

2

Step-by-step solution

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.

3

Final Answer

All answers are correct.

Practice Quiz

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True or false?

One of the angles in a rectangle may be an acute angle.

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