Question

ABCD is a square, P and Q are points on DC and BC respectively, such that AP=DQ, prove that (1) ∆ADP=∆DCQ, (2) angle DMP=90°.​

Answer 1

Step-by-step explanation:

a) In ΔADP and ΔDCQ

AD = DC (Sides of a square are equal)

∠ADP = ∠DCQ = 90degree

AP = DQ (Given)

∴Using RHS congruency rule, ΔADP ΔDCQ

⇒∠DAP = CDQ or ∠1 = ∠3....(1)

b) ∠DMP = ∠1 + ∠2 (Exterior angle property)

= ∠3 + ∠2 (From (1))

= ∠ADP

= 90degree

Hence, proved.