Question

Points M and N are taken on the diagonal AC of a parallelogram ABCD such that AM = CN.
BMDN is a __________.

Answer 1

Given, ABCD is a Parallelogram. M and N are points taken on the diagonal AC such that AM = CN.

Proof:-

We know that the diagonals of a Parallelogram bisect each other. Therefore Ac and BD bisect each other at O.

∴ OC = OA

But CN = AM

∴ OC - CN = OA - AM

⇒ OM = ON

Thus, in quadrilateral BMDN diagonals BD and MN are such that OM = ON and OD = OB, i.e., the diagonal BD and MN bisect each other.

Hence, BMDN is a parallelogram.