2.19 Classifying Parallelograms Bell Ringer 1. WXYZ is a parallelogram. Name an angle congruent to ∠XYZ.                   ∠WZY ∠XWY ∠XWZ ∠ZWY 2. ABCD is a parallelogram. If m∠CDA = 56, then m∠ABC =   .                 66 134 124 56 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Rectangles Definition: A rectangle is a with four right angles. A rectangle is a special type of Thus a rectangle has all the properties of a . Opp. sides are Opp. sides are congruent. Opp. angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other. 2.19 Classifying Parallelograms

Properties of Rectangles Theorem: If a parallelogram is a rectangle, then its diagonals are congruent. Therefore, ∆AEB, ∆BEC, ∆CED, and ∆AED are isosceles triangles. E D C B A Converse: If the diagonals of a parallelogram are congruent , then the parallelogram is a rectangle. 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Examples……. If AE = 3x +2 and BE = 29, find the value of x. If AC = 21, then BE = _______. If m<1 = 4x and m<4 = 2x, find the value of x. If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6. x = 9 units 10.5 units x = 18 units 6 5 4 3 2 1 E D C B A m<1=50, m<3=40, m<4=80, m<5=100, m<6=40 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Rhombus Definition: A rhombus is a parallelogram with four congruent sides. ≡ ≡ Since a rhombus is a parallelogram the following are true: Opp. sides are parallel. Opp. sides are congruent. Opp. angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other 2.19 Classifying Parallelograms

Properties of a Rhombus Theorem: The diagonals of a rhombus are perpendicular. Theorem: Each diagonal of a rhombus bisects a pair of opposite angles. 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Rhombus Examples ..... Given: ABCD is a rhombus. Complete the following. If AB = 9, then AD = ______. If m<1 = 65, the m<2 = _____. m<3 = ______. If m<ADC = 80, the m<DAB = ______. If m<1 = 3x -7 and m<2 = 2x +3, then x = _____. 9 units 65° 90° 100° 10 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Square Definition: A square is a parallelogram with four congruent angles and four congruent sides. Since every square is a parallelogram as well as a rhombus and rectangle, it has all the properties of these quadrilaterals. Opp. sides are parallel. 4 right angles. 4 congruent sides. Consecutive angles are supplementary. Diagonals are congruent. Diagonals bisect each other. Diagonals are perpendicular. Each diagonal bisects a pair of opp. angles. 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Squares – Examples…... Given: ABCD is a square. Complete the following. If AB = 10, then AD = _____ and DC = _____. If CE = 5, then DE = _____. m<ABC = _____. m<ACD = _____. m<AED = _____. 10 units 10 units 5 units 90° 45° 90° 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms Summary Write at least 3 sentences No Homework 2.19 Classifying Parallelograms

2.19 Classifying Parallelograms QUADRILATERAL FAMILY TREE QUADRILATERALS KITE TRAPEZOID PARALLELOGRAMS ISOSCELES TRAPEZOID RECTANGLE RHOMBUS SQUARE 2.19 Classifying Parallelograms