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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 at O.
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Solution
It is given that
BC = AD
BC || AD
We have to prove that AB and CD bisect at O.
If we prove that ΔAOD ≅ ΔBOC , then
We can prove AB and CDbisects atO.
Now in ΔAOD and ΔBOC
AD = BC(Given)
∠OBC =∠OAD (Since AD || BC and AB is transversal)
And ∠OCB = ∠ODA(since AD || BC and CD is transversal)
So by ASAcongruence criterion we have,
ΔAOD ≅ ΔBOC, so
OA = OB
OD = OC
Hence ABand CD bisect each other at O.
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