Question

ABCD is a parallelogram AP and CQ are perpendicular from vertices A and C on diagonal BD show that (1) triangle APB≈ triangle CQD (2) AP=CQ​

Answer 1

Answer:

this the answer that is attached in the file

Answer 2

Answer:

1) ABCD is a parallelogram.

Therefore, DC∥AB.

Now DC∥AB and transversal BD intersects them at B and D.

Therefore, angle ABD=angle BDC (Alternate interior angles).

in triangle APB and triangle CQD, we have.

angle ABP=angle QDC ....(alternate interior angles of parallelogram ABCD and DC∥AB).

angle APB=angle CQD....[each angle 90°].

and AB=CD (Opp. sides of a parallelogram).

Therefore, by AAS criterion of congruence.

triangle APB≈triangle CQD.

2) In triangle APB and triangle CQD,

angle APB=angle CQD (Each 90°).

AB=CD (Opp. sides of parallelogram ABCD).

angle ABP=angle CDQ (Alternate interior angles for AB∥CD).

triangle APB congruent to triangle CQD (By AAS congruency).

AP=CQ by CPCT.

Hence proved.