Question

Line segment AB and CD bisect each other at O . Is ️ triangle AOC congruent to ️ triangle BOD? If yes, state the conditions of congruence? also, give the reason

Answer 1

Answer

Let, this be figure of given condition.

In figure, line segments AB and CD bisect each other at O.

So, O is midpoint of CD and AB

Therefore,

OC=OD

OB=OA

and ∠AOC≅∠BOD⋯⋯[vertically opposite angles]

Hence, by SAS test we can say that

ΔAOC≅ΔBOD

So, yes two triangles are congruent.

Congruence condition used is SAS

Answer 2

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Given,

line segment AB bisect CD

so,

AO = BO

CO = DO

now,

in triangle ACO and triangle BDO

AO = BO (Given)

CO = DO

<1 = <2 (vertical opposite angles)

so,

triangle ACO congruent to BDO by SAS