Question

Given: segment PT || segment QS, segment PT ≅ segment QS, ∠T ≅ ∠S
Prove: ΔPQT ≅ ΔQRS

Answer 1

Segment PT || segment QS,                                  Given

segment PT ≅ segment QS,  

∠T ≅ ∠S

 

Angle TPQ = Angle SQR                      PR is a transversal  cutting parallel segments SQ and TP

                                                             So....it makes corresponding angles TPQ and SQR equal    

 

ΔPQT   ≅    ΔQRS                                ASA congruency