Question

ABCD is a parallelogram and AP and CQ are the perpendiculars from A and C on its diagonal BD, respectively. Prove that AP = CQ.

Answer 1

Given: ABCD is a parallelogram in which BD is diagonal and AP and CQ are drawn perpendiculars to BD from A and C respectively.

To prove: AP = CQ

Proof: Since diagonal of a parallelogram y divides its into two triangles equal in area.

∴ ar (∆ABD) = ar (∆BDC)

⇒ \(\frac { 1 }{ 2 }\) x BD x AP = \(\frac { 1 }{ 2 }\) x BD x QC

⇒ AP = QC

Hence proved.