Question

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

Answer 1

Answer:

A, C, D

Step-by-step 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

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