ABCD is a parallelogram and AP and CQ are perpendicular from vertices A and C on the diagonal BD. show that AP=CQ.
Given: ABCD is a parallelogram. AP and Bd are perpendicular to BD!
To show: AP= CQ
Proof: Consider triangles APB and CQD,
AB = CD (Opp. sides are equal)
angle APB = angle CQB = 90 degree (Given)
angle CDP = angle PBA ( Alternate interior angles, AB is parallel to CD)
Therefore, By SAS congruence,
triangle APB is congruent to tiangle CQD.
Hope this helps!!!