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

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

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

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

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

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

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

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

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

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

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

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