Q2 of 76 Page 10

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.


Given that,


Lines AB and CD intersect at O such that:


BC ‖ AD


And, BC = AD (i)


To prove: AB and CD bisect at O


Proof: In Δ AOD and Δ BOC


AD = BC [From (i)]


∠OBC =∠OAD (AD||BC and AB is transversal)


∠OCB =∠ODA (AD||BC and CD is transversal)


Therefore, by ASA theorem:


Δ AOD ≅ Δ BOC


OA = OB (By c.p.c.t)


And,


OD = OC (By c.p.c.t)


Hence, AB and CD bisect each other at O.


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