Question 1012441: given: segment PR is parallel to segment QS,
angle QPS is congruent to angle RSP
Prove: triangle PQS is congruent to triangle SRP
Answer by ikleyn(52797)   (Show Source):
You can put this solution on YOUR website! .
given: segment PR is parallel to segment QS,
angle QPS is congruent to angle RSP
Prove: triangle PQS is congruent to triangle SRP
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Since angle QPS is congruent to angle RSP, the straight lines PQ and RS are parallel too.
(These angles are alternate interior angles at straight lines PQ and RS and the transverse PS.
See the lesson Parallel lines in this site).
Thus you have the quadrilateral PQSR, in which the pairs of opposite sides are parallel: PR || QS and PQ || RS.
Hence, the quadrilateral is parallelogram.
In a parallelogram, each diagonal divides it in two congruent triangles.
(see the lesson In a parallelogram, each diagonal divides it in two congruent triangles in this site).
The statement is proved.
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