The diagonal BD of a parallelogram ABCD bisects angles B and D. Prove that ABCD is a rhombus.

If the diagonal BD of a quadrillateral ABCD bisects both angleB and angleD . Prove that (AB)/(BC)= (AD)/(CD) .

Two points X and Y lie on the diagonal BD of a parallelogram ABCD such that DX = BY. Prove that squareAXCY is a parallelogram.

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

In Figure, diagonal A C of a quadrilateral A B C D bisects the angles A and C . Prove that A B=A D and C B=CD .

In the figure, diagonal A C of a quadrilateral A B C D bisects the angles A and C . Prove that A B=A D and C B=CD

Prove that the diagonals of a parallelogram bisect each other.

If the diagonals of a parallelogram ABCD are along the lines x+5y=7 and 10x-2y=9 , then ABCD must be a

ABCD is a parallelogram E is mid-point of AB and DE bisects angle D. Prove that BC= BE

if diagonals of a parallelogram bisect each other,prove that its a rhombus

Diagonal AC of a paraleligram ABCD bisects angleA (sec figure). Show that: (i) it bisects angleC also (ii) ABCD is a rhombus.