Answer :

It is given in the question that:

AD and BC are equal perpendiculars to AB

To prove: CD bisects AB

Proof: In ΔAOD and ΔBOC

∠A = ∠B (Perpendicular)

∠AOD = ∠BOC (Vertically opposite angle)

AD = BC (Given)

Therefore,

AAS Postulate (**Angle-Angle-Side**) If two

**angles**and a non-included side of one triangle are congruent to the

**corresponding**parts of another triangle, then the triangles are congruent.

By AAS congruence,

ΔAOD ≅ ΔBOC

Now,

AO = OB (By c.p.c.t)

CD bisects AB

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