Question 1012441
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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 <U>alternate interior angles</U> at straight lines PQ and RS and the transverse PS. 
See the lesson <A HREF=http://www.algebra.com/algebra/homework/Angles/Parallel-lines.lesson>Parallel lines</A> 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 <A HREF=http://www.algebra.com/algebra/homework/Parallelograms/In-a-parallelogram-each-diagonal-divides-it-in-two-congruent-triangles.lesson>In a parallelogram, each diagonal divides it in two congruent triangles</A> in this site).


The statement is proved.
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