Ms. King

1
Ms. Kings Little Bookof Geometry Notes
Period ___
2
Essential QuestionOur Goal

• Can I classify angles? SPI 0606.4.4

3
Types of Angles
Table of Contents

1. Types of Angles
2. Triangle and Quadrilateral
3. Pentagon and Hexagon
4. Heptagon and Octagon
5. Nonagon and Decagon
6. Interior Angle Sum Theorem
7. Missing Interior Angles
8. Exterior Angles Sum
9. Missing Exterior Angles
10. Circles Radius and Diameter
11. Circles p and Circumference
12. Circles Area
13. Surface Area Cylinder
14. Surface Area Pyramids
15. Surface Area Prisms
16. Volume Cylinder
17. Volume Pyramids
18. Volume Prisms

1
4
Essential Question Can I classify angles? SPI
0606.4.4
ACUTE Less than 90

1.
5
ACUTE Less than 90 OBTUSE Greater than 90 less than 180

6
ACUTE Less than 90 OBTUSE Greater than 90 less than 180
RIGHT Exactly 90
7
ACUTE Less than 90 OBTUSE Greater than 90 less than 180
RIGHT Exactly 90 STRAIGHT Exactly 180
8
ACUTE Less than 90 OBTUSE Greater than 90 less than 180
RIGHT Exactly 90 STRAIGHT Exactly 180
COMPLEMENTARY 2 or more Angles that add up to 90

9
ACUTE Less than 90 OBTUSE Greater than 90 less than 180
RIGHT Exactly 90 STRAIGHT Exactly 180
COMPLEMENTARY 2 or more Angles that add up to 90
SUPPLEMENTARY 2 or more Angles that add up to 180
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TYPE OF ANGLES

• Name the type of angle shown

142
11
TYPE OF ANGLES

• Name the type of angle shown

27
12
TYPE OF ANGLES

• Name the type of angle shown

13
TYPE OF ANGLES

• Name the type of angle shown

180
14
TYPE OF ANGLES

• Name the type of angle shown
• What does angle x equal?

x
71
15
TYPE OF ANGLES

• Name the type of angle shown
• What does angle x equal?

37
x
16
TYPE OF ANGLES

• Name the type of angle shown

128
x
What does angle x equal?
17
TYPE OF ANGLES

• Name the type of angle shown

152
x
What does angle x equal?
18
Exit Card Quiz

• Which type of angle is less than 90?
• Which type of angle is equal to 180?
• Which type of angle is greater than 90 but less
  than 180?
• Which type of angle is equal to 90?
• What is the complementary angle to 62?
• What is the value of x?

x
57
21
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Ms. Kings Little Bookof Geometry Notes
Period ___
20
Essential QuestionOur Goal

• How do you find a missing angle measure in
  problems invovling interior/exterior angles
  and/or their sums? SPI 0606.4.2

21
Geometry Notes

• Triangle
• 3 sided POLYGON
• Number of Angles 3
• Interior Angle Sum _____

• Quadrilateral
• 4 sided Polygon
• Number of Angles 4
• Interior Angle Sum _____

2
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Geometry Notes

• Pentagon
• 5 sided POLYGON
• Number of Angles 5
• Interior Angle Sum ___

• Hexagon
• 6 sided POLYGON
• Number of Angles 6
• Interior Angle Sum ___

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23
Geometry Notes

• Heptagon
• 7 sided POLYGON
• Number of Angles 7
• Interior Angle Sum ___

• Octagon
• 8 sided POLYGON
• Number of Angles 8
• Interior Angle Sum ___

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Geometry Notes

• Nonagon
• 9 sided POLYGON
• Number of Angles 9
• Interior Angle Sum ___

• Decagon
• 10 sided POLYGON
• Number of Angles 10
• Interior Angle Sum ___

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25
Interior Angle Sum Theorem
FORMULA (n 2) 180 the total amount of degrees inside (INTERIOR) each type of polygon n (number of sides)
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Missing INTERIOR Angles

• To find a missing interior angle
• Take away all of the angles you do know from the
  interior angle sum.
• Example 1 TRIANGLE (Interior Angle Sum is 180)
  
• 37 105 x 180
• Example 2 QUADRILATERAL (Interior Angle Sum is
  360)
• 32 45 123 X 360

105
37
x
32
45
123
X
7
27
QUICK PRACTICE

• What is the sum of the INTERIOR angles?
• What is the missing angle x? ____________

121
115
126
127
118
X
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QUICK PRACTICE

• What is the sum of the INTERIOR angles?
• What is the missing angle x? ____________

X
101
110
112
106
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EXIT CARD

• Find the missing angle in each polygon
• 1. (n 2) 180
• x ________
• 2.
• x ________

151
75
87
112
x
134
123
x
67
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Ms. Kings Little Bookof Geometry Notes
Period ___
31
Missing EXTERIOR Angles
8

• The SUM of the EXTERIOR angles in ALL polygons
  is 360

How to find a MISSING EXTERIOR ANGLE
EXAMPLE 2
EXAMPLE 1
75
85
x
x
120
142
115
X 75 142 360
X 120 85 115 360
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EXTERIOR ANGLES PRACTICE

• Solve for X

35
42
79
87
24
x
33
EXTERIOR ANGLES PRACTICE

• Find the missing exterior angle of a pentagon
  with four angles of 42, 56, 73, 100

34
EXTERIOR ANGLES PRACTICE

• Solve for X

x
52
35
EXTERIOR ANGLES PRACTICE

• Solve for all missing angles

A ____ B ____ C ____ D _______
A
40
C
D
B
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Ms. Kings Little Bookof Geometry Notes
Period ___
37
ESSENTIAL QUESTIONOUR GOAL

• How do you calculate with circumferences and
  areas of circles?  (SPI 0606.4.4)

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CIRCLES (Radius Diameter)
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RADIUS Half the distance Across the center of a
circle
DIAMETER The distance across The center of a
circle
Radius ( r ) D 2
Diameter ( d ) 2r

1. Diameter is 12 Radius is _____
2. Diameter is 25 Radius is _____
3. Diameter is 3 Radius is ______

1. Radius is 20 Diameter is _____
2. Radius is 4.7 Diameter is _____
3. Radius is 51 Diameter is ______

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Ms. Kings Little Bookof Geometry Notes
Period ___
40
ESSENTIAL QUESTIONOUR GOAL

• How do you calculate with circumferences and
  areas of circles?  (SPI 0606.4.4)

41
CIRCLES Pi (?) and Circumference
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Circumference The distance measure around an
entire circle.
Pi also known as ? about 3.14
FORMULA for finding Circumference of any
circle C ?d or C 2?r
7 in
2 cm
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Finding Circumference
C 2?r or C ?d
3.5 in
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Finding Circumference
C 2?r or C ?d
7.8 in
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Finding Circumference
C 2?r or C ?d
11.05 cm
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Finding Circumference
C 2?r or C ?d
13.7 ft
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Finding Circumference
C 2?r or C ?d
4.2 in
47
Finding Circumference
C 2?r or C ?d
The Circumferenceof the circle is 21.98 cm. a)
What is the diameter? b) What is the radius?
d ?
48
Ms. Kings Little Bookof Geometry Notes
Period ___
49
ESSENTIAL QUESTIONOUR GOAL

• How do you calculate with circumferences and
  areas of circles?  (SPI 0606.4.4)

50
CIRCLES Area
12
Area How much space the circle takesup
(inside) measured in square units
? about 3.14
FORMULA for finding the AREA A ?r2
Example 2
Example 1
8.2 ft
6 cm