Prove PQRS is a parallelogram.?

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1 Answer
CW
Nov 21, 2017

see explanation.

Explanation:

enter image source here
As shown in the figure, a transversal passes through two parallel lines L and M,
As L and M are parallel, the alternate interior angles are equal, => angleASQ=angleDQS=2alpha, and angleBSQ=angleCQS=2beta,
SP, SR, QP and QR are the bisectors of the interior angles,
As 2alpha+2beta=180^@, => alpha+beta=90^@
=> angleSPQ=angleQRS=180-(alpha+beta)=90^@
Hence, S,P,Q,and R form a rectangle.

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