Question

In the figure,ABCD is a parallelogram whose diagonal AC and BD meer at the point O. L and M are Points on AC such that AL=CM.Show that BMDL is a Parallelogram.

Answer 1

in ΔABL and ΔDMC

AB = CD

AL = CM

∠BAL = ∠DCM

∴  ΔABL and ΔDMC

so bl = dm ( by cpct )

similarily using congruency and cpct , all sides and alternate angles would be equal.

finally you would be able to prove bldm as a parallelogram