Question

1. given: pq || st prove: △srt ~ △prq complete the proof by writing the missing reasons. choose from the following list of reasons. (4 pt.) aa triangle similarity sas triangle similarity sss triangle similarity given vertical angles reflexive property corresponding angles alternate interior angles statements reasons (1) pq || st (1) given (2) ∠srt≅∠prq (2) (3) ∠pqr≅∠str (3) (4) △srt~△prq (4)

Explanation:

Step1: Identify angle - relationship for ∠SRT and ∠PRQ

They are the same angle, so by the reflexive property.
Reflexive Property

Step2: Identify angle - relationship for ∠PQR and ∠STR

Since PQ || ST, they are corresponding angles.
Corresponding Angles

Step3: Determine triangle similarity

We have two pairs of congruent angles, so by AA triangle similarity.
AA Triangle Similarity

Answer:

(2) Reflexive Property
(3) Corresponding Angles
(4) AA Triangle Similarity