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

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

Answer 2

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