Question

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

Answer:

Step-by-step explanation:

let LM and BAD intersect at O

as AL = CM and AB = CD

therefore AB-AL=CD-CM

BL = DM ___ (i)

consider ∆OMD and ∆OLB

• <DOM = <BOL (vertically opposite angles)

• <OMD = <OLB (alternate interior angles)

• DM = BL (from i)

therefore ∆OMD congruent to ∆OLB

therefore OM = OL, OD = OB (CPCT)

therefore O bisects LM and BD

therefore LM, BD bisect each other