Hello, whytechocolate!

I'll give you the game plan . . . you fill in the details.

We know that: .AB = CD, AD = BC .(Opposite sides of a parallelogram are equal)Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram,

the parallelogram is a rhombus.

We need to show that two adjacent sides are equal: say, AB = BC.

We know that: .angle A = angle C. .(Opposite angles of a parallelogram are equal)

AC bisects angles A and C.

. . Hence:/1 =/2 =/3

Since/2 =/3, triangle ABC is isosceles.

Therefore: .AB = BC