rhombus (geometry proof): If diagonal bisects angle, then...

[5b2g7k]

I am sure the answer to this is simple, but for some reason I can't get started.

I have been given that ABCD is a parallelogram with <1 congruent to <2 ( Angle BAD that has been bisected). I am to prove that If a dagonal of a parallelogram bisects and angle of the parallelogram, the parallelogram is a rhombus.

The only other angle marked on the diagram is angle 3, which is half of angle BCD, and in the traingle ACB. WHat should be my plan? I know that if I can show angle 3 congruent to angle 2, I can show that all the sides are congruent, but how do I do that? Thanks!

 

[wjm11]

I have been given that ABCD is a parallelogram with <1 congruent to <2 ( Angle BAD that has been bisected). I am to prove that If a dagonal of a parallelogram bisects and angle of the parallelogram, the parallelogram is a rhombus. The only other angle marked on the diagram is angle 3, which is half of angle BCD, and in the traingle ACB. WHat should be my plan?

Since you have a parallelogram, you can use alternate interior angles.

You also have two triangles that are isosceles triangles and are congruent to each other.

Hope that helps.

 

[Deleted member 4993]

I am sure the answer to this is simple, but for some reason I can't get started.

I have been given that ABCD is a parallelogram with <1 congruent to <2 ( Angle BAD that has been bisected). I am to prove that If a dagonal of a parallelogram bisects and angle of the parallelogram, the parallelogram is a rhombus. - What is the definition of rhombus? What is the difference between rhombus and parallelogram?

The only other angle marked on the diagram is angle 3, which is half of angle BCD, and in the traingle ACB. WHat should be my plan? I know that if I can show angle 3 congruent to angle 2, I can show that all the sides are congruent, but how do I do that? Thanks!