Question

use △pqr below to answer the question that follows: which fact is not used to prove that △qor is similar to str? segments st and pq are parallel. angle p is congruent to itself due to the reflexive property. rp is a transversal line passing st and pq. angles rts and rqp are congruent due to the corresponding angles theorem.

Explanation:

Step1: Recall similarity - proof concepts

To prove two triangles similar, we use properties like parallel - lines and corresponding angles.

Step2: Analyze each option

• If segments ST and PQ are parallel, we can use corresponding - angles to prove similarity.
• If PP is a transversal line passing ST and PQ, we can find congruent angles for similarity proof.
• If angles RTS and RQP are congruent (corresponding angles), it helps in similarity proof.
• Angle P being congruent to itself (reflexive property) is not relevant as it is not an angle that relates the two triangles $\triangle QOR$ and $\triangle STR$.

Answer:

Angle P is congruent to itself due to the reflexive property.