Question

anyone pls tell the correct answer for this question ​

Answer 1

Answer:

Given : ABCD is a parallelogram with AP ⊥ BD and CQ⊥ BD

To prove: ΔAPD ≅ ΔCQD

Proof:

Now, AB║DC ( opposite sides of a parallelogram are parallel)

and tranversal BD

∠ ABP=∠CDQ (alternate angles)  .....  (1)

In ΔAPD and ΔCQD

(i) ∠APB = ∠CQD    (90°)

(ii) ∠ ABP=∠CDQ    (given from (1) )

(iii) AB=CD               ( opposite sides of a parallelogram are equal)

∴ ΔAPB≅ΔCQD     ( AAS congruence rule)

⇒ AP = CQ            ( CPCT)