Question

ABCD is a square. p and q are points on DC and BC respectively such that ap =dq. proove that I) ∆ ADP is congruent to ∆ dcq . ii) angle DMP =90°​

Answer 1

Answer:

Diagram I made is the Image below

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

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