Question

17. ABCD is a parallelogram. AP and CQ are
perpendicular to diagonal DB. Prove that
AP= CQ​

Answer 1

Answer:

In the given quadrilateral ABCD,

AP and CQ are perpendiculars.

In the triangle APB and triangle CQD,  as,

AB is parallel to CD.

∠ABP = ∠CDQ (Alternate interior angles)

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

∠APB = ∠CQD = 90° (Right Angles)

Therefore,

ΔAPB ≅ ΔCQD (By ASA Congruence)

Hence, Proved.

(ii).  As,  ΔAPB ≅ ΔCQD. So, from the previous part we can say that,

The corresponding sides of the triangle are also equal.  i.e.

AP = CQ (By CPCT)

Hence, Proved.