Question

ABCD is a squre, P and Q are points on DC AND BC respectively, such that AP = DQ. PROVE THAT
i ∆ ADP = ∆ DCQ
ii angle DMP = 90​

Answer 1

Answer:

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.