# ABCD is a  parallelogram L and M are points on AB and DC respectively such that AL = CM. Show that BD and ML bisect each other.

Given: In a parallelogram ABCD, AL = CM
To Prove: DP = PB and MP = PL
Proof: Since DC and AB are two opposite sides of parallelogram ABCD
... AB = DC  .............(1)
Also AL = CM  ...........(2) (1) − (2) ⇒ AB - AL = DC - CM ⇒ LB = DM
Now in ΔDMP and ΔBLP,
we have
∠1 = ∠4...... (Alternate Interior angles)
∠2 = ∠3...... (Alternate Interior angles)
and DM = BL
... ΔDMP ≅ ΔBLP
... DP = PB and MP = PL....(c.p.c.t.)
... BD and ML bisect each other.

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