need help with geometry.?

Question

If a diagonal of a parallelogram busects an angle of a parallelogram, the parallelogram is a rhombus.
(State your plan and give a proof)
Given: ABCD is a parallelogram w/ angle1~= angle2.
To Prove: ABCD is a rhombus.
Plan:
Please help!

Answer 1

Use graph paper and graph out this parallelogram..
A(-6,0) B(0,10) C(6,0) D(0,-10)
Angle A = ang C (definition of parallelogram)
Angle B = ang D (def. of para)
The diagonals bisect the angles(given)
The diagonals bisect each other(def. of Para)
Using side-angle-side you can prove all the triangles formed by the diagonals are congruent. So that means all sides of parallelogram are equal and you have a rhombus.