Question

every rhombus is a parallelogram prove that

Answer 1

because 4 sides and diagonals are equal

Answer 2

A parallelogram is a quadrilateral (a closed area with 4 straight sides) where the opposite sides are parallel. This forces the opposite sides to have the same length, but adjacent sides need not have the same length. A rhombus requires adjacent sides have the same length, and in fact have all sides the same length.

When visualizing these two dimensional structures, it is easy to even define a rhombus as parallelogram with equal length sides. One could further define a rectangle as a parallelogram with a 90 degree angle. This forces all interior angles to be 90 degrees. And you probably guessed it, a square is a rhombus with a 90 degree angle…

Just as a square is a rectangle with equal length sides, so is a rhombus a parallelogram with equal length sides. Alternatively, a rhombus with 90 degree internal adjacent angles is a square, and a parallelogram with 90 degree internal adjacent angles is a rectangle.

This is not a proof, but I think this answers the underlying question.