SOLUTION: Question: 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 par

Algebra ->  Geometry-proofs -> SOLUTION: Question: 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 par      Log On


   

Question 38152: Question:
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 <1~= <2
To Prove: ABCD is a rhombus
So I can see that angles 1 and 2 are equal.
In theorm 5-13 says the diagonals are pependicular but there is only one and then therom 5-14 says that each diagnoal... bisects two angles of the rhombus. Am I making this too difficult or do I just need to state 5-14
Thanks
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
THIS IS NOT CORRECT.THERE IS SOME THING WRONG IN YOUR HYPOTHESIS.DIAGONALS OF A PARALLELOGRAM DEFINITELY BISECT THEIR ANGLES ,WHETHER IT IS A RHOMBUS OR NOT.THE DIAGONALS NEED TO BE PERPENDICULAR TO EACH OTHER FOR IT TO BE A RHOMBUS