According to the diagram below, which similarity statements are true? Check all that apply

Question

asked Jan 15, 2020 193k views

2 Answers

Bruno Lubascher · Answer 1 · 2020-01-19T23:25:30+0000

Answer:

A, C, D

Explanation:

Consider right triangles PQS, PRQ and QRS. In these triangles,

$m\angle QPS=m\angle QPR=m\angle SQR\\ \\m\angle QSR=m\angle PQR=m\angle QSR$

So, by AA theorem,

$\triangle PQS\sim \triangle PRQ\sim \triangle QRS$

From this statement, strictly follow options A and D

$\triangle PQR\sim \triangle PSQ\\ \\\triangle PQS\sim \triangle QRS$

Option B is false, because PRS is not a triangle

Option C is true, because

$\triangle PRQ\sim \triangle QRS\Rightarrow \triangle PQR\sim \triangle QSR$