1. 2.19 - Classify Parallelograms 1 Ringer Bell 1) 2) 12/10/09

2. 2.19 - Classify Parallelograms 2 2.19 Classify Parallelograms

3. 2.19 - Classify Parallelograms 3 Rectangles Opp. sides are ||. Opp. sides are. Opp. Angles are. Consecutive angles are supplementary. Diagonals bisect each other. Definition:A rectangle is a parallelogram with four right angles. A rectangle is a special type of parallelogram. Thus a rectangle has all the properties of a parallelogram.

4. 2.19 - Classify Parallelograms 4 Properties of Rectangles Therefore, ∆ AEB, ∆ BEC, ∆ CED, and ∆ AED are isosceles triangles. If a parallelogram is a rectangle, then its diagonals are congruent. E D C B A Theorem: Converse: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

5. 2.19 - Classify Parallelograms 5 Examples……. 1.If AE = 3x +2 and BE = 29, find the value of x. 2.If AC = 21, then BE = _______. 3. If m<1 = 4x and m<4 = 2x, find the value of x. 4.If m<2 = 40, find m<1, m<3, m<4, m<5 and m<6. m<1=50, m<3=40, m<4=80, m<5=100, m<6=40 10.5 units x = 9 units x = 18 units 6 5 4 32 1 E D C B A

6. 2.19 - Classify Parallelograms 6 Rhombi & Squares

7. 2.19 - Classify Parallelograms 7 Rhombus Definition:A rhombus is a parallelogram with four congruent sides. Since a rhombus is a parallelogram the following are true: Opposite sides are parallel. Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. Diagonals bisect each other ≡ ≡

8. 2.19 - Classify Parallelograms 8 Properties of a Rhombus Theorem: The diagonals of a rhombus are perpendicular. Theorem: Each diagonal of a rhombus bisects a pair of opposite angles.

9. 2.19 - Classify Parallelograms 9 Rhombus Examples..... Given: ABCD is a rhombus. Complete the following. 1.If AB = 9, then AD = ______. 2.If m<1 = 65, the m<2 = _____. 3.m<3 = ______. 4.If m<ADC = 80, the m<DAB = ______. 5.If m<1 = 3x -7 and m<2 = 2x +3, then x = _____. 9 units 65° 90° 100° 10

10. 2.19 - Classify Parallelograms 10 Square Opposite sides are parallel. Four right angles. Four congruent sides. Consecutive angles are supplementary. Diagonals are congruent. Diagonals bisect each other. Diagonals are perpendicular. Each diagonal bisects a pair of opposite angles. 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.

11. 2.19 - Classify Parallelograms 11 Squares – Examples…... Given: ABCD is a square. Complete the following. 1.If AB = 10, then AD = _____ and DC = _____. 2.If CE = 5, then DE = _____. 3.m<ABC = _____. 4.m<ACD = _____. 5.m<AED = _____. 10 units 5 units 90° 45° 90°

12. 2.19 - Classify Parallelograms 12 Homework All four assignments are due tomorrow. NO EXCEPTIONS