Theorems 6-1 through 6-13

Theorem 6-9

Each diagonal of a rhombus bisects two angles of the rhombus

Theorem 6-3

The diagonals of a parallelogram bisect each other

Theorem 6-11

The diagonals of a rectangle are congruent

Theorem 6-10

The diagonals of a rhombus are perpendicular

Theorem 6-8

If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 6-7

If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram

Theorem 6-12

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

Theorem 6-6

If one pair of opposite sides of a quadrilateral is congruent and parallel, then the quadrilateral is a parallelogram

Theorem 6-14

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

Theorem 6-13

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

Theorem 6-5

If the diagonals of a quadrilateral are both congruent and parallel, then the quadrilateral is a parallelogram

Theorem 6-4

If three or more parallel lines cut off congruent segments on one transversal, then they cut of congruent segments on every transversal

Theorem 6-2

Opposite angles of a parallelogram are congruent

Theorem 6-1

Opposite sides of a parallelogram are congruent