Question

ABCD is a quadrilateral in which AP and CQ are perpendicular to diagonal BD and AP=CQ.prove that BD bisects AC.​

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.

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