Question

ABCD is a square.P and A are any points in side AB and B.C. respectively Of AQ=DP prove AQ And DP are perpendicular to each other ​

Answer 1

a) In ΔADP and ΔDCQ

AD = DC (Sides of a square are equal)

∠ADP = ∠DCQ = 900

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

= 900

Hence, proved.