Question

two lines AB and CD intersect at o such that bc is equal and parallel to ad . prove that the lines ab and cd bisect 0

Answer 1

Step-by-step explanation:

In order to prove that AB and CD bisect each other at O, it is sufficient to prove that ΔAOD≅ΔBOC.

In these two triangles,

we have

AD=BC

∠OBC=∠OAD [∵AD∥BC and AB is transversal]

and, ∠OCB=∠ODA [∵AD∥BC and CD is transversal]

So, by ASA congruence criterion, we obtain

ΔAOD≅ΔBOC

⇒OA=OB and OD=OC

⇒ AB and CD bisect each other at O.

solution

Answer 2

Step-by-step explanation:

In order to prove that AB and CD bisect each other at O, it is sufficient to prove that ΔAOD≅ΔBOC.

In these two triangles,

we have

AD=BC

∠OBC=∠OAD [∵AD∥BC and AB is transversal]

and, ∠OCB=∠ODA [∵AD∥BC and CD is transversal]

So, by ASA congruence criterion, we obtain

ΔAOD≅ΔBOC

⇒OA=OB and OD=OC

⇒ AB and CD bisect each other at O.

solution