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