Q. 53.5( 4 Votes )
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,
∠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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