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Two lines A B\ a n d\ C D intersect at O...

Two lines `A B\ a n d\ C D` intersect at `O` such that `B C` is equal and parallel to `A Ddot` Prove that the lines `A B\ a n d\ C D` bisect at `O`

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In order to prove that AB and CD bisect each other at O
It is sufficient to prove that, `/_\AOD~=/_\BOC`
In these two triangles,we have`AD=BC`
`/_OBC=/_OAD(AD∥BC and AB is transversal)`
`/_OCB=/_ODA (AD∥BC and CD is transversal)`
So, by ASA congruence criterion, we obtain`/_\AOD~=/_\BOC`
`OA=OB andOD=OC`
`AB and CD`, bisect each other at O.
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