Prove PQRS is a parallelogram.?

enter image source here

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.

Related questions
Impact of this question
2679 views around the world
You can reuse this answer
Creative Commons License