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Quadrilaterals and Parallelograms

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- 1. SECTION 5-6 Quadrilaterals and Parallelograms
- 2. ESSENTIAL QUESTIONS How do you classify different types of quadrilaterals? What are the properties of parallelograms, and how do you use them? Where you’ll see this: Construction, civil engineering, navigation
- 3. VOCABULARY 1. Quadrilateral: 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
- 4. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
- 5. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
- 6. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
- 7. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: 6. Consecutive Sides:
- 8. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: Sides in a quadrilateral that do not touch each other 6. Consecutive Sides:
- 9. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: A quadrilateral with two pairs of parallel sides 3. Opposite Angles: In a quadrilateral, the angles that do not share sides 4. Consecutive Angles: Angles in a quadrilateral that are “next” to each other; they share a side 5. Opposite Sides: Sides in a quadrilateral that do not touch each other 6. Consecutive Sides: Sides in a quadrilateral that do touch each other
- 10. QUADRILATERAL HIERARCHY
- 11. QUADRILATERAL HIERARCHY Quadrilateral
- 12. QUADRILATERAL HIERARCHY Quadrilateral 4 sides
- 13. QUADRILATERAL HIERARCHY Quadrilateral 4 sides Trapezoid
- 14. QUADRILATERAL HIERARCHY Quadrilateral 4 sides Trapezoid 1 pair parallel sides
- 15. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 4 sides Trapezoid 1 pair parallel sides
- 16. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Trapezoid 1 pair parallel sides
- 17. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Trapezoid 1 pair parallel sides
- 18. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sides
- 19. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sides
- 20. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides
- 21. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides Square
- 22. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, 4 equal Trapezoid 90° angles sides 1 pair parallel sides Square 4 equal sides 4 90° angles
- 23. PROPERTIES OF PARALLELOGRAMS
- 24. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent
- 25. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent
- 26. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementary
- 27. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementary 4.The sum of the angles is 360°
- 28. DIAGONALS OF PARALLELOGRAMS
- 29. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other
- 30. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent
- 31. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent 7. Diagonals of a rhombus are perpendicular
- 32. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
- 33. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
- 34. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
- 35. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
- 36. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC.
- 37. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. 6 6
- 38. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. 6 6 x=3
- 39. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 6 6 x=3
- 40. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 6 6 x=3
- 41. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 6 6 x=3
- 42. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 6 x=3
- 43. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3
- 44. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3 AC = 24
- 45. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. a. If AE = 5x - 3 and EC = 15 - x, find AC. AE = EC = 15 − 3 = 12 AC = AE + EC 6 AC = 12 + 12 6 x=3 AC = 24 units
- 46. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB.
- 47. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1
- 48. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 −4y +1 −4y +1
- 49. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 −4y +1 −4y +1 2=y
- 50. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = −4y +1 −4y +1 2=y
- 51. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 −4y +1 −4y +1 2=y
- 52. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 2=y
- 53. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y
- 54. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9
- 55. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9 DB = 18
- 56. EXAMPLE 1 In parallelogram ABCD, diagonals AC and BD intersect at E. b. If DE = 4y + 1 and EB = 5y - 1, find DB. 4y + 1 = 5y − 1 DE = EB = 4(2) + 1 = 9 −4y +1 −4y +1 DB = DE + EB 2=y DB = 9 + 9 DB = 18 units
- 57. EXAMPLE 2 a. In quadrilateral ABCD, diagonals AC and BD intersect at E. What special quadrilateral must ABCD be so that AED is an isosceles triangle? Draw a picture first.
- 58. EXAMPLE 2 a. In quadrilateral ABCD, diagonals AC and BD intersect at E. What special quadrilateral must ABCD be so that AED is an isosceles triangle? Draw a picture first. Class poll and discussion
- 59. EXAMPLE 2 b. In rectangle ABCD, diagonals AC and BD intersect at E. Which pair of triangles is not congruent? Draw a picture first.
- 60. EXAMPLE 2 b. In rectangle ABCD, diagonals AC and BD intersect at E. Which pair of triangles is not congruent? Draw a picture first. Class poll and discussion
- 61. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ c. m∠XYW d. ZW
- 62. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. c. m∠XYW d. ZW
- 63. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW
- 64. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW 45°
- 65. EXAMPLE 2 c. A woodworker makes parallel cuts XY and ZW in a board. The edges of the board, XZ and YW are also parallel. YW = 21.5 in. Find each measure, if possible. a. XZ b. m∠YXZ 21.5 in. 135° c. m∠XYW d. ZW 45° Not enough info
- 66. HOMEWORK
- 67. HOMEWORK p. 218 #1-43 odd “Make visible what, without you, might perhaps never have been seen.” - Robert Bresson

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