SOLUTION: I need a two-column proof for the following: PROVE:If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. (State your plan and g

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Question 163332: I need a two-column proof for the following:
PROVE:If a diagonal of a parallelogram bisects an angle of the parallelogram, the parallelogram is a rhombus. (State your plan and give a proof.)
GIVEN:ABCD is a parallelogram with angle 1 congruent to angle 2.
TO PROVE: ABCD is a rhombus.
PLAN: ??????
Thanks in advance...Joanne
Answer by elima(1433) (Show Source):
You can put this solution on YOUR website!
It is hard to prove without seeing the figure to know where the angles are, but I'll give it a try;
I am assuming <1 and <2 are opposite angles, if they are;
Theorem:
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
Plan: You can use SAS or SSS to find congruent triangles.Then use the congruent parts to help you prove the theorem.
I hope this helps
:)