Given that ΔPQR is similar to ΔPTS, which statement MUST be true? A) m∠PST = m∠QPR B) m∠TPS = m∠RPQ C) m∠SPT = m∠PTS D) m∠PRQ = m∠PTS

Question

Mathematics

Gauge Underwood

15 June, 10:37

Given that ΔPQR is similar to ΔPTS, which statement MUST be true? A) m∠PST = m∠QPR B) m∠TPS = m∠RPQ C) m∠SPT = m∠PTS D) m∠PRQ = m∠PTS

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Answers (1)

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Izaiah Benton · Answer 1

Answer: B) m∠TPS = m∠RPQ

Step-by-step explanation:

Given that ΔPQR is similar to ΔPTS

We know that of two triangles are similar then their corresponding angles are equal in measure and corresponding sides are proportional.

Therefore, If ΔPQR is similar to ΔPTS, then

m∠TPS=m∠RPQ

m∠STP=m∠RQP

m∠PTS=m∠PQR

Therefore, from the given options, only B is the right options, i. e. m∠TPS = m∠RPQ