List statements and proofs that show that PQ is congruent to RS. I will give brainliest to best answer

Given - PS is parallel to QR

angle QPS is congruent to angle SRQ

To prove - PQ is congruent to RS

Solution -

In triangle PSQ and SQR

Angle PSQ = Angle SQR ( Interior Angle form by the parallel lines are equal i.e PQ is parallel to QR)

Angle P = Angle R (given)

SQ = SQ ( common)

PSQ = SQR ( prove above)

By ASA Congruence criteria Triangle PQS is congruent to triangle QRS

By CPCT PS is congruent to RS

Hence, Proved

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