Question

AD and BC are equal and perpendicular to line segment AB. show that CD bisects AB​

Answer 1

Hii here is the answer:--✍️

It is given in the question that:

AD and BC are equal perpendiculars to AB

To prove: CD bisects AB

Proof: In ∆AOD and ∆ BOC

∠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,

Now,

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

CD bisects AB

Hope it helps you ❣️☑️☑️☑️☑️

Answer 2

Given AD = BC
To show CD bisect
In ∆ OAD and ∆ OBC
<1 = <2 (V.O.A)
<3=<4 each 90°
<DA = <BC ( given )
By AAS Congruent rule
OA = OB (CPCT)
CD bisect AB
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