1. Parallelogram Definition
Quadrilaterals Unit - Parallelograms
Parallelogram Definition
A quadrilateral with both pairs of opposite sides parallel

2. Theorem 8.3 Q R P S
If a quadrilateral is a parallelogram, then its opposite sides are congruent.
If PQRS is a parallelogram, then
QP = RS and QR = PS

3. Theorem 8.4 Q R P S
If a quadrilateral is a parallelogram, then its opposite angles are congruent.
If PQRS is a parallelogram, then
<P = <R and <Q = <S

4. Theorem 8.5
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.
If PQRS is a parallelogram, then
xº + yº = 180º Q R P S xº yº

5. Theorem 8.6
If a quadrilateral is a parallelogram, then its diagonals bisect each other.
QM = MS and
PM = MR Q R P S M

6. Types of Parallelograms
Rhombus– A parallelogram with four congruent sides Rectangle-A parallelogram with four right angles Square-A parallelogram with four congruent sides and four right angles

7. Rhombus Corollary
A quadrilateral is a rhombus if and only if it has four congruent sides.
ABCD is a rhombus if and only if
AB = BC =CD = AD A B D C

8. Rectangle Corollary
A quadrilateral is a rectangle if and only if it has four right angles.
ABCD is a rectangle if and only if
<A, <B, <C, and <D are right angles A B D C

9. Square Corollary
A quadrilateral is a square if and only if it is a rhombus and a rectangle.
ABCD is a square if and only if
AB = BC =CD = AD
and <A, <B, <C, and <D are right angles. A B D C

10. Theorem 8.11
A parallelogram is a rhombus if and only if its diagonals are perpendicular.
ABCD is a rhombus if and only if AC is perpendicular to BD A B D C

11. Theorem 8.12
A parallelogram is a rhombus if and only if each diagonal bisects a pair of opposite angles.
ABCD is a rhombus if and only if AC bisects <BAD and <BCD and BD bisects <ABC and <ADC. A B D C

12. Theorem 8.13
A parallelogram is a rectangle if and only if its diagonal are congruent.
ABCD is a rectangle if and only if
AC = BD A B D C