2. Triangles Triangles Triangles Let’s Discover: Triangle Cut-Apart

3. What do you know about triangles?

4. Characteristics of triangle “angles”: The sum of the angles in any size triangle is equal to 180 0. 90 55 35 90 + 35 + 55 = 180

5. Example 1: 80 45x

6. Example 2:

7. Now try these:

11. In triangle ABC, m ∠ CAB = 57 and m ∠ ABC = 104. Find m ∠ ACB.

12. If you have angles 30 and 80 degrees, what is the measure of the third angle?

14. Angles Angles Angles Brainpop Video “Types of Triangles”

15. Characteristics of triangle “sides”: The sum of the two smaller sides must be greater than the length of the third side.

16. Example 1: Can the following lengths make a triangle? 4 cm, 8 cm, 14 cm 4 + 8 = 12 12 ‹ 14 so no these sides cannot make a triangle.

17. Can the following lengths make a triangle? 5 in, 10 in, 13 in Example 2: 5 + 10 = 15 15 › 13 so these sides do make a triangle.

18. Does the following lengths form a triangle? a.7 ft, 19 ft, 15 ft b.24 mm, 20 mm, 30 mm c.15 in, 25 in, 45 in d.4 cm, 12 cm, 18 cm e.1 yd, 10 yd, 20 yd

19. Exit Card: 3-2-1

20. http://www.youtube.com/watch?v=GO20ZgUzlc0

25. Let’s have some fun!! IXL - Identify complementary, supplementary, vertical, adjacent, and congruent angles (8th grade math practice)

26. Exit Card: One minute talk about differences in angle relationships with a partner.

27. Lesson 4 Supplementary And Complementary

28. How do you use supplementary angles to find unknown angle measures? For Example What is the measure angle x in the figure below? 110 o x o

29. Let’s Review Core Lesson A set of stairs inclines at a 110 o angle. A support beam is g oing to be constructed under the stairs. What angle m easure does the support need to have? 110 o x o Any interior ray from a p oint on a straight angle c reates two s upplementary angles.

30. Let’s Review Core Lesson 110 o x o 110 o + x = 180 o x = 70 o Supplementary angles add to 180 o. -110 o

31. Let’s Review Core Lesson Two angles are supplementary. If one angle measure is 82 o, what is the measure of the second angle? x + 82 o = 180 o - 82 o -82 o x = 98 o

32. Let’s Review Guided Practice Find the measure of angle x below. 158 o x o

33. Let’s Review Extension Activities Andy measured two angles. One angle was 153 o and one angle was 47 o. Andy said that the two angles were supplemental. Is Andy correct? Explain your reasoning.

34. How do you use complementary angles to find unknown angle measures? For example What is the measure of angle x? xoxo 15 o

35. Let’s Review A right angle measures exactly 90 o. 90 o

36. Core Lesson Two angles are complementary. If the measure of one angle is 43 o, what is the measure of the second angle? 43 o + x = 90 o -43 o -43 o x = 47 o 43 o x

37. Let’s Review Guided Practice Two angles are complementary. If one a ngle measures 17 o, what is the measure o f the second angle?

38. Let’s Review Extension Activities Two angles are complementary. One angle measures x o and the second angle measures (x + 16) o. Find the measures of the two angles.

39. Let’s Review Quick Quiz Two angles are complementary. One angle measures 22 o. What is the measure of the second angle? The two angles below are complementary. What is the measure of the missing angle? 63 o x o

40. Exit Card: What is the difference in supplementary and complementary angles?

41. CIRCLES

42. Circle Review:  A circle is the set of points that are all an equal distance from a point called the center.  The diameter is twice the radius. d = 2r  The radius is half of the diameter. r = d/2.  Pi (π) is approximately 3.14  Circumference of a circle can be found using C = πd or C = 2πr  Area of a circle can be found using the formula A = πr 2

44. Mr. Smith has a garden that is in the shape of a circle. There is a path 5 feet in length that goes from the center of the garden to the edge of the garden. If Mr. Smith wants to add a path across the garden, how long will it be? Radius (r) Diameter (d)

45. The diameter is twice the radius. d = 2r The radius is half of the diameter. r =

46. Since d = 2r d = 2(5ft) d = 10ft

47. Find the radius of a circle that has a diameter of 7 inches. r = r = r =3.5 inches

48. A circle has a radius of 12 meters. What is the diameter of the circle?

49. Find the radius of a circle with a diameter of 15 centimeters. A circle has a diameter of 12 feet. What is the length of the radius?

50. How do you find the circumference of a circle?

51. Pi, represented by the symbol π, is a constant ratio that relates circumference and diameter. Pi is approximated as 3.14 To find the circumference, we use one of the formulas: C = π d or C = 2πr

52. What is the circumference of a circle that has a radius of 8 centimeters? Do not approximate pi. C = 2πr C = (2) π (8 cm) C = 16 π cm

53. A circle has a radius of 6 inches. What is the circumference of the circle? Do not approximate pi.

54. A circle has a diameter of 8 meters. What is the circumference of the circle? Use 3.14 for pi. A circle has a radius of 7 feet. Find the circumference of the circle. Do not approximate pi.

55. How do you find the area of a circle?

56. Area of a circle can be found by using the formula A = πr 2

57. A pizza has a radius of 9 inches. What is the area of the pizza? r = 9 inches

58. A = π(9in.) 2 A = 3.14(81in. 2 ) A = 254.34in. 2

59. Find the area of a circle with a diameter of 10 meters. Do not approximate pi. A = π(5m) 2 A = 25 π m 2

60. What is the area of a circle that has a radius of 6 cm? Use 3.14 for pi.

61. Susan drew a circle with a radius of 4 inches and Ellen drew a circle with a radius of 8 inches. Ellen said “since the radius of my circle with twice the radius of your circle, the area of my circle is twice the area of your circle.” Is Ellen’s statement correct? If not, explain what Ellen could say instead.

62. A circle is inside of a square, as shown below. The edges of the square each touch a point on the circle. If the square has an area of 16 square meters, what is the area of the circle?

63. A circular pizza can feed 4 people if it has an area of at least 200 square inches. A pizza from Joe’s Pizza has a radius of 9 inches. Is it enough to feed a family of 4?

64. How do you find the area of the circle if you only know the circumference?

65. Area of a Circle = πr 2 Circumference of a Circle= πd or 2πr

66. A playground in the shape of a circle has a circumference of 18π yards. What is the area of the playground? C = 18π yds. C = πd D = 18 yds 18 yds

67. Area = π (9 yds) 2 Diameter = 18 yards Radius = 9 yards Area = 81 π yds 2 18 yds 9 yds

68. A circle has an approximate circumference of 37.68 cm. If 3.14 was used for pi, what is the area of the circle? C = πd 37.68cm = 3.14d 37.68cm = 3.14d 3.14 3.14 d = 12 cm

69. d = 12 cm r = 6 cm A = 3.14(6cm) 2 A = 3.14(36cm 2 ) A = 113.04 cm 2 A circle has an approximate circumference of 37.68 cm. If 3.14 was used for pi, what is the area of the circle?

70. The circumference of a circle is 10 π. What is the area of the circle?

71. The circumference of a circle is 12.56 ft ². If 3.14 was used to approximate pi, what is the area of the circle? A circle has a circumference of 9 π meters. Find the area of the circle.

72. How can you find the circumference of a circle if you only know the area?

73. Area of a Circle = πr 2 Circumference of a Circle= πd or 2πr

74. The reverse of squaring a number is finding the square root. 3 2 = 9

75. Bill has a circular garden that he wants to put a fence around. He knows that the area of a garden is 16π yds 2. How much fencing does Bill need to go around the circumference of the garden? A = 16π yds 2 A = πr 2 C = 2πr r 2 = 16 yds 2 r = 4 yds 4 yds C = 2π(4 yds) C = 8π yds

76. A circle has an area of 25π cm 2. What is the circumference of the circle?

77. The area of a circle is 16 π meters 2. Stephanie concluded that the circumference of the circle would be 16 π. She stated “the radius would be 8 meters since the square root of 16 is 8.” What mistake did Stephanie make. Write an explanation describing how to fix her mistake.

78. A circle inside of a square touches the square at each edge as shown below. If the circle has an area of 25 π feet 2, find the area of the square.

79. Find the circumference of the circle that has an area of 81π m 2. A circle has an area of 113.04 cm 2. What is the circumference of the circle?