ms. king’s little book of geometry notes period ___
TRANSCRIPT
Ms. King’s Ms. King’s LittleLittle Book Book
of of Geometry NotesGeometry Notes
Period ___Period ___
Essential Question“Our Goal”
Can I classify angles? SPI: 0606.4.4
Table of ContentsTable of Contents
1. Types of Angles2. Triangle and Quadrilateral3. Pentagon and Hexagon4. Heptagon and Octagon5. Nonagon and Decagon6. Interior Angle Sum Theorem7. Missing Interior Angles8. Exterior Angles Sum9. Missing Exterior Angles10.Circles: Radius and Diameter11.Circles: π and Circumference12.Circles: Area13.Surface Area: Cylinder14.Surface Area: Pyramids15.Surface Area: Prisms16.Volume: Cylinder17.Volume: Pyramids18.Volume: Prisms
1
Types of AnglesTypes of Angles
ACUTE
Less than 90˚Less than 90˚
Essential Question: Can I classify angles? SPI: 0606.4.4
1.
ACUTE
Less than 90˚Less than 90˚
OBTUSE
Greater than 90˚; less than 180Greater than 90˚; less than 180˚̊
ACUTE
Less than 90˚Less than 90˚
OBTUSE
Greater than 90˚; less than 180Greater than 90˚; less than 180°°
RIGHT
Exactly 90˚Exactly 90˚
ACUTE
Less than 90˚Less than 90˚
OBTUSE
Greater than 90˚; less than 180Greater than 90˚; less than 180°°
RIGHT
Exactly 90˚Exactly 90˚
STRAIGHT
Exactly 180˚Exactly 180˚
ACUTE
Less than 90˚Less than 90˚
OBTUSE
Greater than 90˚; less than 180Greater than 90˚; less than 180°°
RIGHT
Exactly 90˚Exactly 90˚
STRAIGHT
Exactly 180˚Exactly 180˚
COMPLEMENTARY:COMPLEMENTARY: 2 or more Angles that add up to 90˚90˚
ACUTE
Less than 90˚Less than 90˚
OBTUSE
Greater than 90˚; less than 180Greater than 90˚; less than 180˚̊
RIGHT
Exactly 90˚Exactly 90˚
STRAIGHT
Exactly 180˚Exactly 180˚
COMPLEMENTARY:COMPLEMENTARY: 2 or more Angles that add up to 90˚90˚
SUPPLEMENTARY:SUPPLEMENTARY: 2 or more Angles that add up to 180˚180˚
TYPE OF ANGLES
Name the type of angle shown:
142˚
TYPE OF ANGLES
Name the type of angle shown:
27˚
TYPE OF ANGLES
Name the type of angle shown:
TYPE OF ANGLES
Name the type of angle shown:
180˚
TYPE OF ANGLESName the type of angle shown:
What does angle x equal?
71˚
x˚
TYPE OF ANGLESName the type of angle shown:
What does angle x equal?
37˚
x˚
TYPE OF ANGLES
Name the type of angle shown:
128˚ x˚
What does angle x equal?
TYPE OF ANGLES
Name the type of angle shown:
152˚x˚
What does angle x equal?
Exit Card QuizExit Card Quiz
1. Which type of angle is less than 90°?
2. Which type of angle is equal to 180°?
3. Which type of angle is greater than 90° but less than 180°?
4. Which type of angle is equal to 90°?
5. What is the complementary angle to 62°?
6. What is the value of x?57°21°
x°
Ms. King’s Ms. King’s LittleLittle Book Book
of of Geometry NotesGeometry Notes
Period ___Period ___
Essential Question“Our Goal”
How do you find a missing angle measure in problems invovling interior/exterior
angles and/or their sums? SPI: 0606.4.2
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
Geometry Notes Pentagon
* 5 sided POLYGON
Number of Angles: 5
Interior Angle Sum: ___
Hexagon
* 6 sided POLYGON
Number of Angles: 6
Interior Angle Sum: ___
3
Geometry Notes Heptagon
* 7 sided POLYGON
Number of Angles: 7
Interior Angle Sum: ___
Octagon
* 8 sided POLYGON
Number of Angles: 8
Interior Angle Sum: ___
4
Geometry Notes Nonagon
* 9 sided POLYGON
Number of Angles: 9
Interior Angle Sum: ___
Decagon
* 10 sided POLYGON
Number of Angles: 10
Interior Angle Sum: ___
5
Interior Angle Sum Theorem
FORMULA: n = (number of sides)
(n – 2) • 180 =
the total amount of degrees inside (INTERIOR) each type of polygon
6
Missing INTERIOR AnglesMissing 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˚
37˚
105˚
x˚
32˚
123˚
45˚
X˚7
QUICK PRACTICEQUICK PRACTICEWhat is the sum of the INTERIOR angles?
What is the missing angle x? ____________
121˚ 115˚
126˚127˚
118˚ X˚
QUICK PRACTICEQUICK PRACTICEWhat is the sum of the INTERIOR angles?
What is the missing angle x? ____________
X˚
101˚
112˚106˚
110˚
EXIT CARDEXIT CARDFind the missing angle in each polygon:
1. (n – 2)• 180
x = ________
2.
x = ________
123˚ 134˚
67˚ x˚
112˚
87˚
151˚75˚
x˚