Mathematics
Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN. Prove that BMDN is a parallelogram.
Answer
Join BD. Let BD intersect AC at point O.
In parallelogram ABCD,
Diagonals of || gm bisect each other.
⇒ OA = OC ………(1)
⇒ OB = OD
Given,
⇒ AM = CN ………(2)
Subtracting equation (2) from (1), we get :
⇒ OA - AM = OC - CN
⇒ OM = ON.
In quadrilateral BMDN,
⇒ OM = ON and OB = OD.
∴ Diagonals of quadrilateral BMDN bisect each other.
∴ BMDN is a parallelogram.
Hence, proved that BMDN is a parallelogram.
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