Properties of Parallelograms Chapter 6 Section 6.2 Properties of Parallelograms

Transitive Symmetric Substitution

Some Properties of Parallelograms Definition Definition Parallelogram A parallelogram is quadrilateral with both pairs of opposite sides parallel

No, Only one pair of opposite sides are parallel Some Properties of Parallelograms No, Only one pair of opposite sides are parallel Yes, both pairs of opposite sides are parallel

No, The polygon is a hexagon Some Properties of Parallelograms No, The polygon is a hexagon

Some Properties of Parallelograms Theorem Theorem 6.2 If a quadrilateral is a parallelogram, then both pairs of opposite sides are congruent

W  Y and X  Z Some Properties of Parallelograms Theorem If a quadrilateral is a parallelogram, then both pairs of opposite angles are congruent W  Y and X  Z

mW + mX = 180 mX + mY = 180 mY + mZ = 180 mZ + mW = 180 Some Properties of Parallelograms Theorem Theorem 6.4 If a quadrilateral is a parallelogram, then consecutive angles are supplementary mW + mX = 180 mX + mY = 180 mY + mZ = 180 mZ + mW = 180

KJGH with diagonals Some Properties of Parallelograms Theorem If a quadrilateral is a parallelogram, then its diagonals bisect each other KJGH with diagonals

= 10.15 = 13 = XO + ON = 3 + 3 = 6 = KP + PX + XR = PX = XR = 5 Some Properties of Parallelograms = 13 = 10.15 = XO + ON = 3 + 3 = 6 = KP + PX + XR = 5 + 5 + 5 = 15 = LX +XN = 6 + 6 =12 = PX = XR = 5

= mKLN = 68.3 = 50.7 = mNKL = 61 = 68.3 = KN + NM + LM + KL Some Properties of Parallelograms = mKLN = 68.3 = 50.7 = mNKL = 61 = 68.3 = KN + NM + LM + KL = 13 + 10.15 + 13 + 10.15 = 46.3

Opposite sides are congruent Some Properties of Parallelograms Opposite sides are congruent 5x = 3x + 18 2x = 18 x = 9 3y – 7 = 2y + 4 y – 7 = 4 y = 11

Opposite angles are congruent Some Properties of Parallelograms Opposite angles are congruent 3x – 18 = 2x + 12 x – 18 = 12 x = 30 Consecutive angles are Supplementary 4y + 72 = 180 4y = 108 y = 27 3z + 72 = 180 3z = 108 z = 36 2(30) + 12 72

Diagonals Bisect Each Other Some Properties of Parallelograms Diagonals Bisect Each Other 7y – 2 = 5y + 4 2y – 2 = 4 2y = 6 y = 3 3x + 2 = 23 3x = 21 x = 7

Applications of Parallelogram Properties

Applications of Parallelogram Properties

HW #67 Pg 333-334 8-36