1. Ms. King’s Little Book of Geometry Notes
Period ___

2. Essential Question “Our Goal”
Can I classify angles? SPI:

3. Types of Angles Table of Contents Types of Angles
Triangle and Quadrilateral
Pentagon and Hexagon
Heptagon and Octagon
Nonagon and Decagon
Interior Angle Sum Theorem
Missing Interior Angles
Exterior Angles Sum
Missing Exterior Angles
Circles: Radius and Diameter
Circles: π and Circumference
Circles: Area
Surface Area: Cylinder
Surface Area: Pyramids
Surface Area: Prisms
Volume: Cylinder
Volume: Pyramids
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. COMPLEMENTARY: 2 or more Angles that add up to 90˚
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. COMPLEMENTARY: 2 or more Angles that add up to 90˚
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˚

10. 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: x˚ 71˚
What does angle x equal? x˚
71˚

15. TYPE OF ANGLES Name the type of angle shown: 37˚ x˚
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: x˚ 152˚
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°
21°
57°

19. Ms. King’s Little Book of Geometry Notes
Period ___

20. Essential Question “Our Goal”
How do you find a missing angle measure in problems invovling interior/exterior angles and/or their sums? SPI:

21. Geometry Notes Triangle Quadrilateral * 4 sided Polygon
Number of Angles: 3
Interior Angle Sum: _____
Quadrilateral
* 4 sided Polygon
Number of Angles: 4
Interior Angle Sum: _____ 2

22. Geometry Notes Pentagon Hexagon * 5 sided POLYGON * 6 sided POLYGON
Number of Angles: 5
Interior Angle Sum: ___
Hexagon
* 6 sided POLYGON
Number of Angles: 6
Interior Angle Sum: ___ 3

23. Geometry Notes Heptagon Octagon * 7 sided POLYGON * 8 sided POLYGON
Number of Angles: 7
Interior Angle Sum: ___
Octagon
* 8 sided POLYGON
Number of Angles: 8
Interior Angle Sum: ___ 4

24. Geometry Notes Nonagon Decagon * 9 sided POLYGON * 10 sided POLYGON
Number of Angles: 9
Interior Angle Sum: ___
Decagon
* 10 sided POLYGON
Number of Angles: 10
Interior Angle Sum: ___ 5

25. Interior Angle Sum Theorem
FORMULA:
(n – 2) • 180 =
the total amount of degrees inside (INTERIOR) each type of polygon
n = (number of sides) 6

26. 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˚)
x = 180˚
Example 2: QUADRILATERAL (Interior Angle Sum is 360˚)
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˚

28. QUICK PRACTICE What is the sum of the INTERIOR angles?
What is the missing angle x? ____________ X˚
110˚
101˚
106˚
112˚

29. EXIT CARD Find the missing angle in each polygon: 1. (n – 2)• 1802.
151˚
75˚
87˚
112˚ x˚
134˚
123˚ x˚
67˚

30. Ms. King’s Little Book of Geometry Notes
Period ___

31. Missing EXTERIOR Angles8
**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 = 360˚
X = 360˚

32. 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˚

36. Ms. King’s Little Book of Geometry Notes
Period ___

37. ESSENTIAL QUESTION: “OUR GOAL”
How do you calculate with circumferences and areas of circles?  (SPI: )

38. CIRCLES (Radius & Diameter)10
CIRCLES (Radius & Diameter)
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
Diameter is 12: Radius is _____
Diameter is 25: Radius is _____
Diameter is 3: Radius is ______
Radius is 20: Diameter is _____
Radius is 4.7: Diameter is _____
Radius is 51: Diameter is ______

39. Ms. King’s Little Book of Geometry Notes
Period ___

40. ESSENTIAL QUESTION: “OUR GOAL”
How do you calculate with circumferences and areas of circles?  (SPI: )

41. CIRCLES: Pi (Π) and Circumference11
CIRCLES: Pi (Π) and Circumference
Circumference: The distance measure around an entire circle.
Pi also known as Π = about 3.14
FORMULA for finding Circumference of any circle:
C = Πd or C = 2Πr
7 in
2 cm

42. Finding Circumference
C = 2Πr or C = Πd
3.5 in

43. Finding Circumference
C = 2Πr or C = Πd
7.8 in

44. Finding Circumference
C = 2Πr or C = Πd
11.05 cm

45. Finding Circumference
C = 2Πr or C = Πd
13.7 ft

46. Finding Circumference
C = 2Πr or C = Πd
4.2 in

47. Finding Circumference
C = 2Πr or C = Πd
The Circumference of the circle is cm.
a) What is the diameter?
b) What is the radius?
d = ?

48. Ms. King’s Little Book of Geometry Notes
Period ___

49. ESSENTIAL QUESTION: “OUR GOAL”
How do you calculate with circumferences and areas of circles?  (SPI: )

50. 12
CIRCLES: Area
Area: How much space the circle takes up (inside) measured in square units
Π = about 3.14
FORMULA for finding the AREA:
A = Πr2
Example 2
Example 1
8.2 ft
6 cm

51. Ms. King’s Little Book of Geometry Notes
Period ___

52. ESSENTIAL QUESTION: “OUR GOAL”
How can you determine the surface area and volume of prisms, pyramids, and cylinders?  (SPI: )

53. Surface Area: CYLINDER13
*The area of a 3-dimensial object
*Cylinder: 2 circular bases, and a rectangle.
**FORMULA:
(2Πr2) + (2Πr • h)
3 cm
7 cm