ABCD is a parallelogram. L and M are points on AB and DC respectively and AL=CM. Prove that LM and BD bisect each other.

Answer 1

Let the intersection of BD and LM be P.

Now,
AL = CM so BL = DM
m<ABD = m<CDB
m<BLM = m<DML

So, by ASA, LBP and MDP are congruent triangles.

S, LP = PM and DB bisects LM

Similarly, DP=BP and LM bisects BD

Answer 2

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