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

asked Jul 5, 2019 124k views

2 Answers

John Dorian · Answer 1 · 2019-07-12T04:07:12+0000

Answer:

The correct option is B.

Explanation:

Two triangle are similar if their corresponding sides are in the same proportion or the corresponding angles are same.

It is given that the ΔPQR is similar to ΔPTS. It means all corresponding angles are same.

$\angle R=\angle S$

$\angle Q=\angle T$

$\angle P=\angle P$

Angle P can be defined as

$\angle QPR=\angle TPS$

$\angle RPQ=\angle TPS$

Therefore option B is correct.

$\angle PST\\eq\angle QPR$

$\angle SPT\\eq\angle PTS$

$\angle PRQ\\eq\angle PTS$

Therefore option A, C and D are incorrect.