Question

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

Answer 1

Answer:

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).

Hope it will be helpful :)

Answer 2

Explanation:

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.