SOLUTION: Prove: if diagonal of a parallelogram bisects an angle of the parallelogram, then the parallelogram is a rhombus.(state plan and give proof) Given: ABCD is a parallelogram with

Question 391009: Prove: if diagonal of a parallelogram bisects an angle of the parallelogram, then the parallelogram is a rhombus.(state plan and give proof)
Given: ABCD is a parallelogram with <1 congruent <@.
To prove: ABCD is a rhombus.
Plan:__________________?

i need help with the proofs and reasons...im not very good at this at all! thank youu so much

Heres a picture!
http://i1189.photobucket.com/albums/z426/cwallace2/Casey002.jpg
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Since AD || BC, angle 1 = angle 3, so you can replace the "3" with a "1." Also, since angle 2 = angle 1 (already given), AB = BC, and since AB = CD and BC = AD (the parallel sides of a parallelogram are congruent), all four sides are congruent to each other and it's a rhombus.

I almost never use the two-column proof when writing solutions to proof problems...it helps you back up each statement with a reason, but virtually no mathematicians use the two-column proof when explaining a proof(e.g. in a paper).
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