Question

Prove that the diagonals of the rhombus bisect the interior angles.

Answer 1

Draw a rhombus ABCD. Draw a diagonal BD.
All sides AB, BC, CD, DA are congruent by definition of rhombus.
BD is a common side, so triangles ABD and CBD are congruent (SSS).

I will leave it to you to complete the proof that BD bisects angles ABC and CDA.

You can prove similarly that AC bisects angles DAB and BCD.