Question

Bella is planning a proof for the Isosceles Triangle Theorem using the following information and diagram. Given: APQR is an isosceles triangle with base PR Prove: ZP ZR First, she draws the angle bisector of ZQ and labels it QB. She plans to show that ZP and ZR are corresponding parts of congruent triangles. Which congruence criterion can be used in her proof to show that APQB ARQB? A. ASA B. SAS C. SSS

Answer 1

Similar triangles may or may not be congruent.

The congruent criterion to use in her proof is (b) SAS theorem

From the question, we understand that she draws an angle bisector from $\mathbf{\angle Q}$ to side PR

This means that, either sides of angle Q are congruent. (this is represented by A i.e. angle)

When $\mathbf{\angle Q}$ is bisected, sides PB and RB become congruent

i.e. $\mathbf{PB \cong RB}$ ... (this is represented by S i.e. side)

Lastly, both triangles share a common side at QB .. (this is also represented by S i.e. side)

So, we have: SAS

Hence, the congruent criterion to use in her proof is (b) SAS theorem

Read more about similar and congruent triangles at:

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