# 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 ->  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

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 Geometry: Proofs in Geometry Solvers Lessons Answers archive Quiz In Depth

 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 ThanksAnswer by venugopalramana(3286)   (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