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# Integrated Math 2 Section 5-6

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• ### Integrated Math 2 Section 5-6

1. 1. SECTION 5-6 Quadrilaterals and Parallelograms
2. 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. 3. VOCABULARY 1. Quadrilateral: 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
4. 4. VOCABULARY 1. Quadrilateral: A four-sided figure 2. Parallelogram: 3. Opposite Angles: 4. Consecutive Angles: 5. Opposite Sides: 6. Consecutive Sides:
5. 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. 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. 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. 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. 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
14. 14. QUADRILATERAL HIERARCHY Quadrilateral 4 sides Trapezoid 1 pair parallel sides
15. 15. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 4 sides Trapezoid 1 pair parallel sides
16. 16. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Trapezoid 1 pair parallel sides
17. 17. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Trapezoid 1 pair parallel sides
18. 18. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sides
19. 19. QUADRILATERAL HIERARCHY Parallelogram Quadrilateral 2 pairs parallel 4 sides sides Rectangle Rhombus Opposite sides congruent, Trapezoid 90° angles 1 pair parallel sides
20. 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. 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. 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. 23. PROPERTIES OF PARALLELOGRAMS
24. 24. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent
25. 25. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent
26. 26. PROPERTIES OF PARALLELOGRAMS 1. Opposites sides are congruent 2.Opposite angles are congruent 3.Consecutive angles are supplementary
27. 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. 28. DIAGONALS OF PARALLELOGRAMS
29. 29. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other
30. 30. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent
31. 31. DIAGONALS OF PARALLELOGRAMS 5.Diagonals bisect each other 6.Diagonals of a rectangle are congruent 7. Diagonals of a rhombus are perpendicular
32. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 66. HOMEWORK
67. 67. HOMEWORK p. 218 #1-43 odd “Make visible what, without you, might perhaps never have been seen.” - Robert Bresson