Question

ABCD is a square.P and Q are points on DC and BC respectively, such that AP=DQ . Prove that ∆ADP=~ ∆DCQ .

Answer 1

Given:ABCD is a square.P and Q are points on DC and BC respectively,such that AP=DQ.∆ADP=~∆DCQ

RTP:∆ADP=~∆DCQ

Proof:In ADP and DCQ

AP=DQ

<ADC=<DCQ(90°)

AD=DC

by SAS rule

ADP is congruent to DCQ

<DAP=<CDQ