Question

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

Answer 1

given

ABCD is a ||gm

AL=CM

⇒ BL= DM(as AB=CD and 1/2AB= 1/2CD)

to prove

LM bisects BD

proof

as BL= DM, AL=CM therefore L and M are midpoint

consider tri ABD

LO || AD, LO= 1/2 AD (mid point theorem)

consider tri BCD

MO || BC, MO= 1/2 BC (mid point theorem)

consider tri LOM and tri DOM

LB = DM (proved above)

< LBO = < MDO (alternate interior angles)

< LOM = < MOD (vertically opposite angles)

therefore LOM ≅ DOM

hence,

LO = MO (cpct)

BO = DO (cpct)

hence proved

Answer 2

Answer:

Hope it helps you.....