document.write( "Question 1012441: given: segment PR is parallel to segment QS,
\n" ); document.write( " angle QPS is congruent to angle RSP
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Algebra.Com's Answer #628378 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "given: segment PR is parallel to segment QS,
\n" ); document.write( " angle QPS is congruent to angle RSP
\n" ); document.write( "Prove: triangle PQS is congruent to triangle SRP
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document.write( "Since angle QPS is congruent to angle RSP, the straight lines PQ and RS are parallel too. \r\n" );
document.write( "(These angles are alternate interior angles at straight lines PQ and RS and the transverse PS. \r\n" );
document.write( "See the lesson Parallel lines in this site).\r\n" );
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document.write( "Thus you have the quadrilateral PQSR, in which the pairs of opposite sides are parallel: PR || QS and PQ || RS.\r\n" );
document.write( "Hence, the quadrilateral is parallelogram.\r\n" );
document.write( "In a parallelogram, each diagonal divides it in two congruent triangles.\r\n" );
document.write( "(see the lesson In a parallelogram, each diagonal divides it in two congruent triangles in this site).\r\n" );
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document.write( "The statement is proved.\r\n" );
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