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

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
:)
RELATED QUESTIONS
Prove: if diagonal of a parallelogram bisects an angle of the parallelogram, then the... (answered by richard1234)

Question: Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, (answered by venugopalramana)

Prove: If a diagonal of a parallelogram bisects an angle of the parallelogram, the... (answered by Edwin McCravy)

I need help with a two column proof for the following: If the diagonals of a trapezoid... (answered by ikleyn)

Given: Parallelogram ABCD Use a two column proof to prove that angle B and angle D are... (answered by Alex.33)

Thank you for your help in advance. Choose a proof to complete from the options below. (answered by MathLover1)

Prove: If an isosceles triangle has an altitude from the vertex to the base, then the... (answered by Edwin McCravy)

PQRS is a parallelogram with PQ=PS. Prove that RP bisects the angle QPS (answered by ikleyn)

I have a proof and shown is quadrilateral ABCD. On the figure the diagonals AC and DB are (answered by solver91311)