Question

Que: AD and BC are equal perpendiculars to a line segment AB. Show that CD bisects AB.​

Answer 1

Solution:

Given, AD and BC are two equal perpendiculars to AB.

To prove: CD is the bisector of AB

Proof:

Triangles ΔAOD and ΔBOC are similar by AAS congruency

Since:

• (i) ∠A = ∠B (perpendicular angles)
• (ii) AD = BC (given)
• (iii) ∠AOD = ∠BOC (vertically opposite angles)

∴ ΔAOD ≅ ΔBOC.

So, AO = OB ( by CPCT).

Thus, CD bisects AB (Hence proved).

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Answer 2

Answer:

In triangle OAD & OBC

AD=BC (GIVEN)

<OAD=<OBC (EACH=90*)

<AOD=<BOC (VERTICLE OPP ANGLE)

THEREFORE,

TRIANGLE ODA=OCB (AAS CRITERIA)

OA=OB (CPCT)

So, CD bisects AB.