Q5 of 40 Page 8

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.

More from this chapter

All 40 →
3 In a ΔABC, lines are drawn through A, B and C parallel to sides BC, CA and AB respectively forming a triangle PQR. Prove that BC = QR.
 4 ABCD is a parallelogram AB is produced to E so that BE = AB. Show that ED bisects BC.
 6 ΔABC and ΔDEF are two triangles such that AB, BC are respectively equal and parallel to DE, EF; show that AC is equal and parallel to DF.
7 AB, CD are two parallel lines and a transversal l intersects AB at G and CD at H. Prove that the bisectors of the interior angles form a parallelogram, with all the angles are right angles.