| A | B |
|---|
| Theorem 6-5 | If both pairs of opposite sides of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
| Theorem 6-6 | If both pairs of opposite angles of a quadrilateral are congruent, then the quadrilateral is a parallelogram |
| Theorem 6-7 | If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. |
| Theorem 6-8 | If one pair of opposite sides of a quadrilateral is both parallel and congruent, then the quadrilateral is a parallelogram. |
| Parallelogram Property Summary | 1. Both pairs of opposite sides are parallel.2. Both pairs of opposite sides are congruent. 3. Both pairs of opposite angles are congruent. 4.Diagonals bisect each other. 5.A pair of opposite sides is both parallel and congruent. |
| Theorem 6-9 | If a parallelogram is a rectangle, then its diagonals are congruent |
| Theorem 6-10 (Converse of Thm 6-9) | If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle. |
| Rectangle Property Summary | 1. Opposite sides are congruent and parallel. (All parallelograms) 2. Opposite angles are congruent. (All parallelograms) 3. Consecutive angles are supplementary. (All parallelograms) 4. Diagonals bisect each other. (All parallelograms) 5.Diagonals are congruent. (Rectangle) 6.All four angles are right angles. (Rectangle) |
| Theorem 6-11 | The diagonals of a rhombs are perpendicular |
| Theorem 6-12 (Converse of Thm 6-11) | If the diagonals of a parallelogram are perpendicular, |
| Theorem 6-13 | Each diagonal of a rhombus bisects a pair of opposite angles. |
