Question

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

Answer 1

Statements

1. QR ⊥ PT

2. <QRP and <SRT are right angles

3. <QPR ≈ <STR

4. <QRP ≈ <SRT

5. △TSR ~ △PQR

Reasons

1. Given

2. def. of perpendicular

3. Given

4. all right angles are ≈

5. AA similarity theorom

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Answer 2

Answer: B) m∠TPS = m∠RPQ

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