Theorem 6-9:

Each diagonal of a rhombus bisects two angles of the rhombus.

Theorem 6-10:

The diagonals of a rhombus are perpendicular.

Theorem 6-11:

The diagonals of a rectangle are congruent.

Theorem 6-12:

If one diagonal of a parallelogram bisects two angles of the parallelogram, then the parallelogram is a rhombus.

Theorem 6-13:

If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

Theorem 6-14:

If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.