However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right.

There exists a pair of similar, but not congruent, triangles.

This will use the theory of congruent triangles.

The same odd numbers are now arranged in two different ways in congruent triangles.

One diagonal is a line of symmetry (it divides the quadrilateral into two congruent triangles).

Using congruent triangles, one can prove that the rhombus is symmetric across each of these diagonals.

It is constructed by congruent right triangles with 4, 8, and 10 triangles meeting at each vertex.

Each diagonal divides the quadrilateral into two congruent triangles.

The illustration on the right shows four congruent triangles generated by translations along the arrow.

As in spherical geometry the only similar triangles are congruent triangles.