2. Objective: students will be able to understand the basics concepts of geometry and be able to apply them to real world problems.

3.  Angles  Triangles  Circles  3-D Shapes  Area  Volume  Surface Area

4. Let’s Get Started!!!

5. Objective: to be able to examine relationships between pairs of angles, examine relationships of angles formed by parallel lines and a transversal.

6. Vertical Angles  When two lines intersect, they form two pairs of opposite angles.  Angles are congruent. Model 4 1 2 3 & & Symbol

7. Adjacent Angles  When two angles have the same vertex between them, share a common side, and do not overlap. Model 4 1 2 3 & & Symbol & are adjacent angles

8. Complementary Angles  When two angles have the sum of 90 o Model 35 o 65 o Symbol 35 o + 65 o = 90 o

9. Supplementary Angles  When two angles have the sum of 180 o Model 35 o 145 o Symbol 35 o + 145 o = 180 o

10. Perpendicular Lines  When two lines intersect to form a right angle. Model

11. Jan is cutting a corner off a piece of rectangular tile. Classify the relationship between angle x and angle y. If the m y = 135 o, what is the measure of x?

12. The following pairs of angles are congruent. Alternate Interior Angles: are on opposite sides of the transversal and inside the parallel lines. Angles 3 & 5, Angles 4 & 6 Alternate Exterior Angles: are on opposite sides of the transversal and outside the parallel lines. Angles 1 & 7, Angles 2 & 8 Corresponding Angles: are in same position on the parallel lines in relation to the transversal Angles 1 & 5, Angles 2 & 6, 2 1 4 7 5 8 6 3 Parallel Line Transversal Line (a line that intersects two parallel lines. When a transversal intersects it forms 8 angles. Interior and exterior angles.

13. Using the figure from page 496, answer the following questions. a.) Classify the relationship between angle 3 and angle 5. Since angle 3 and angle 5 are alternate interior angles they are congruent. b.) If the measure of angle 1 is 120 degrees, the find the measure of angle 5 and angle 3. Since angle 1 and angle 5 are corresponding angles, they are congruent and angle 5 measures 120 degrees. Since angle 5 and angle 3 are congruent, angle 3 measures 120 degrees also.

14. Using the figure in the book, answer the following questions. Measure of angle ABD = 164 o Find the measures of angle ABC and CBD. (2x + 23) o XoXo A C D B

15. Open Your Books Way to Go!

17. All Triangles Have 3 Names!

18. First Middle Last

19. Let’s look at the first names…

20. ACUTE

21. 3 acute angles that measure less than 90 

22. OBTUSE

23. 1 obtuse angle that measures greater than 90 

24. RIGHT

25. 1 right angle that measures 90 

26. Let’s look at the middle names…

27. SCALENE

28. No equal sides

29. ISOSCELES

30. 2 equal sides Shows that the sides are of equal length

31. EQUILATERAL

32. 3 equal sides Shows that the sides are of equal length

33. Let’s look at the last name…

34. TRIANGLE

35. Let’s look at some examples…

36. What is the full name of this triangle?

37. Obtuse, Scalene, Triangle!

38. What is the full name of this triangle?

39. Acute, Isosceles, Triangle!

40. What is the full name of this triangle?

41. Acute, Equilateral, Triangle!

42. Looking Good, let’s play…

43. Awesome Job!

44. NAME THAT TRIANGLE!!

45. Here are some simple rules:  Everyone will be in teams chosen by the teacher.  Everyone will have a turn at writing the answer.  Each player will write the answer of their choosing WITHOUT the help from their teammates. That means NO TALKING DURING EACH ROUND.  Negative comments will result in loss of points.  Talking DURING rounds will result in loss of points.

46. LET’S PLAY!!

48. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

49. Acute Equilateral Triangle

51. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

52. Obtuse Isosceles Triangle

54. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

55. Obtuse Scalene Triangle

57. 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1

58. Right Scalene Triangle

59. GREAT JOB EVERYONE!!! Do we need a tie breaker?

60. Let’s find the measures of triangles!

61. All triangles measure 180 

62. What do they measure? 180 

63. 71  64 o X Let’s find x.

64. 71  64 o X 64 o + 71 o = 135 o 180 o - 135 o = 45 o x = 45 o

65. 38 o Let’s find x.

66. 38 o 90 o + 38 o = 128 o 180 o - 128 o = 52 o x = 52 o X

67. Now, find the measures of the triangles!

68. 40 o Let’s find x. X

69. 40 o X = 50 o X

70. 40 o Let’s find x. X 25 o

71. 40 o X = 115 o X 25 o

72. 60 o Let’s find x. X60 o

73. X = 60 o X60 o

74. Let’s put our new information to the test and start our assignment for the day!

75. Circle Time!

76.  Radius  Diameter  Central Angle  Chord  Semi Circle

77. What is it?  A segment that connects the center point of a circle to the circumference of the circle A B

78. How do you name it?  You name a radius like a line segment starting with the center point first.  Example: AB A B

79. What is it?  A segment that passes the center of a circle and has both endpoints on the circumference of the circle B C A

80. How do you name it?  You name a diameter just like a line segment do not name the center point.  Example: CB or BC B C A

81. What is it?  A segment that has both endpoints on the circumference of the circle C B

82. How do you name it?  You name a chord just like you would a line segment.  Example: BC or CB C B

83. Objective: to be able to use the formulas for circumference and area to solve real world problems.

84. ∏ Intro to Pi Video

85. ∏ = 3.14159…

86. Pi is an irrational number.  Meaning, it goes on forever and never repeats  So far, mathematicians have discovered over 134 million digits of pi  They’re still working to find more…

87. But, all you need to know is… ∏ = 3.14

88.  Pi is a ratio of circumference (C) to diameter (d) C/d = ∏

89.  Circumference is the distance around a circle  Circumference is measured in units

90. C = (d) ∏ or C =(2) (r) ∏

91. Find the circumference… C = 10 3.14 C = 31.4 m 10 m

92. Find the circumference… C = 2 2 3.14 C = 12.56 in 2 in

93. Find the circumference… C = 2 8 3.14 C = 50.24 yd 8 yd

94. Find the circumference… C = 2 3.14 C = 6.28 cm 2 cm

95. Great! Now let’s move on to area!

96.  Area is the number of square units that fit inside a circle  Area is measured in units 2

97. A = ∏ r 2

98. Can also be written… A = ∏ r r

99. Find the area… A = 3.14 6 6 A = 113.04 km 2 6 km

100. Find the area… A = 3.14 4 4 A = 50.24 mi 2 8 mi

101. Find the area… A = 3.14 15 15 A = 706.5 m 2 15 m

102. Find the area… A = 3.14 3.5 3.5 A = 38.465 ft 2 7 ft

103. Super work!!!

104. So how does this apply in the real world?

105.  Social Studies: ◦ The circular base of the teepees of the Sioux and Cheyenne tribes have a diameter of about 15 ft. What is the area of the base to the nearest square unit? ◦ r = 15 ÷ 2 ◦ r = 7.5 ft. ◦ A = 3.14 7.5 7.5 ◦ A = 176.625 ◦ A ≈ 177 ft 2

106.  Technology: ◦ Airport Surveillance Radar (ASR) tracks planes in a circular region around an airport. What is the area covered by the radar if the diameter of the circular region is 120 nautical miles? ◦ r = 120 ÷ 2 ◦ r = 60 nautical miles ◦ A = 3.14 60 60 ◦ A = 11304 square nautical mi

107.  Archaeology: ◦ The large stones of Stonehenge are arranged in a circle about 30 m in diameter. How many meters would you have to walk if you wanted to walk the entire distance around the structure? ◦ d = 30 m ◦ C = 30 3.14 ◦ C = 94.2 m

108. Way to go!

109. Objective: to be able to find area of composite figures and use that process to solve real life problems.

110. Square/ Rectangle L W 4 ft 7 ft 9 cm 28 ft 2 81 cm 2

111. Triangle ½ b h 5 ft 4 ft 10 ft 2

112. Circle 3.14 r 2 113.04 in 2 6 in

113. 4.3 m 9.2 m 19.78 m 2 7.25 m 3 m 21.75 m 2

114. 19.625 m 2 15 m 225 m 2 5 cm

116. Parallelogram b h 5 ft 7 ft 4 ft 35 ft 2

117. Parallelogram b h 6 ft 12 ft 4 ft 72 ft 2

118. Parallelogram b h 2.5 in 8 in 3.5 in 28.0 in 2

119. Trapezoid Just a reminder…name the only characteristic that trapezoids have. 1 set of parallel sides

120. Trapezoid ½ h(b 1 + b 2 ) 4 in 7 in 2 in 11 in 2

121. Trapezoid ½ h(b 1 + b 2 ) 10 in 4 in 6 in 32 in 2

122. Trapezoid ½ h(b 1 + b 2 ) 23 in 17 in 9 in 180 in 2

124. Composite Figures are made up of two or more shapes. To find the area of a composite figure, you must decompose the figure into shapes with areas that you know and then find the sum of these areas!

125. Find the area of the composite figure.  The area can be separated into a semicircle and a triangle.  ½ (3.14)(r 2 ) for circle  ½ (b)(h) for triangle 6m6m 11 m 14.1 m 33 m+ 47.1 m 2 =

126. Find the area of the composite figure.  The area can be separated into a trapezoid and a rectangle.  ½ h (b 1 + b 2 ) for trapezoid  L W for square 20 m 82.5 m 400 m +482.5 m 2 = 20 m 25 m 13 m

128. Pedro’s father is building a shed. How many square feet of wood is needed to build the back of the shed shown at the right? 15 ft 12 ft 4 ft 210 ft 2

129. Find the area of each shape and subtract. 4 cm 3 cm 13 cm 7 cm

131. Objective: to be able to find the volume of certain 3-D shapes to solve real world problems.

132.  Volume of a three-dimensional figure is the number of cubic units needed to fill the space inside the figure.  A cubic unit is a cube with edges 1 unit long 1 cm

133.  To solve for volume…. area of the base the height

134.  Measured in cubic feet…. cm 3

135. length width height L W H

136.  Let’s Try It 12 6 8 = 576 cm 3

137. Let’s Try Some on Your Own!!

138. ½ base height width H B W

139.  Let’s Try It ½ 8 10 60 = 2400 cm 3

141. Let’s Try Some on Your Own!!

142. 3.14 radius radius height

143.  Let’s Try It 3.14 5 5 14 = 14 5 1,099 cm 3

144. Let’s Try Some Word Problems!!!

145. A semi has a trailer that is 32 inches long, 12 inches wide and 22 inches high. What is the volume of the trailer?

146. A tent has the shape of a triangular prism. From the floor to the peal is 9 feet. The floor is 22 feet wide and 35 feet long. What is the volume of the tent?

147. A bucket has a diameter of 20 centimeters and a height of 15 centimeters. What is the volume?

148. You are sooo good!