Question

two line segments AB and CD bisect each other at O. show that triangleAOC congruent to triangleBOD​

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

Above written two pairs of equal sides and one pair of equal angles are three equality relations of matching parts used to arrive at answer

pls mark as BRAINLIST

Answer 2

Answer:

Step-by-step explanation:

AB and CD bisect each other at O i.e, AO=BO and CO=DO

in ΔCOA and ΔDOB

Given CO=OD,∠COA=∠BOD [ vertically opp angles]

AD=BD

∴ΔCOA≅ΔBOD

(i) ∴AC=BD[C.P.CT]

(ii) ∠CAB=∠ABD[C.P.CT]

again

in ΔCOB and ΔAOD

CO=OD [given]

BO=AO [given]

∠COB=∠AOD [vertically opp angles]

∴ΔCOB≅ΔAOD

∴∠CBA=∠BAD [ C.P. C.T]

(iii) and so AD∣∣CD [ ∵∠CBA=∠BAD which are altanate angles]

and AD=CB [C.P.C.T]