Question

The parallelogram has the angle measuers shown. Can you conclude that it is a rhombus, a rectangle, or a square? Explain.
So I'm going to describe the image then I'll give what I think would be a correct answer to explain. (I'm really bad at this)

Description: There's a triangle on top of an identical triangle but upside down, so the bottom of each triangle is touching. The bottom-left angle (top triangle) says 72 degrees, and the bottom-right (top triangle) says its also 72 degrees. The measurements for the bottom triangle are the same.

I think that it's a rhombus because a square would have parallel sides. The diagonals are perpendicular bisectors of each other, and the diagonals bisect the angles. It's not a rectangle either because a rectangle has parallel sides, opposite sides are congruent. And the properties of a rhombus is that the sides are parallel, opposite angles are congruent, and consecutive angles are supplementary.

Does my answer answer the question correctly?