Prove PQRS is a parallelogram.?

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1 Answer
CW
Nov 21, 2017

see explanation.

Explanation:

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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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