Symmetries of Rhombi

Imagine a square fastened with very loose fasteners at the corners. It can squash and tilt into a parallelogram. That parallelogram is called a rhombus. The rhombus still has equal opposite corner angles, and it still has equal side lengths. Take a look at the diagram below:

Say it's a rhombus. (It's not actually one in terms of side lengths and angles.) $\angle ACB$ has the same measure as $\angle ADB$, and angles $\angle CAD$ and $\angle CBD$ also have equal measures.

These are all the symmetries of a rhombus.

A rhombus has two lines of reflexive symmetry. It also has 180 degree rotational symmetry about it's center.