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

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

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: π 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 Types of Angles

ACUTE Less than 90˚ Essential Question: Can I classify angles? SPI:

ACUTE Less than 90˚ OBTUSE Greater than 90˚; less than 180˚

ACUTE Less than 90˚ OBTUSE Greater than 90˚; less than 180° RIGHT Exactly 90˚

ACUTE Less than 90˚ OBTUSE Greater than 90˚; less than 180° RIGHT Exactly 90˚ STRAIGHT Exactly 180˚

ACUTE Less than 90˚ OBTUSE Greater than 90˚; less than 180° RIGHT Exactly 90˚ STRAIGHT Exactly 180˚ COMPLEMENTARY: 90˚ 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: 90˚ COMPLEMENTARY: 2 or more Angles that add up to 90˚ SUPPLEMENTARY: 180˚ SUPPLEMENTARY: 2 or more Angles that add up to 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 ANGLES Name the type of angle shown: What does angle x equal? 71˚ x˚x˚

TYPE OF ANGLES Name the type of angle shown: What does angle x equal? 37˚ x˚x˚

TYPE OF ANGLES Name the type of angle shown: 128˚ x˚x˚ What does angle x equal?

TYPE OF ANGLES Name the type of angle shown: 152˚x˚x˚ What does angle x equal?

Exit 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°x°

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

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

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 – 2) 180 = the total amount of degrees inside (INTERIOR) each type of polygon n = (number of sides) 6

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˚ 37˚ 105˚ x˚x˚ 32˚ 123˚ 45˚ X˚X˚ 7

QUICK PRACTICE What is the sum of the INTERIOR angles? What is the missing angle x? ____________ 121˚115˚ 126˚ 127˚ 118˚X˚X˚

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

EXIT CARD Find the missing angle in each polygon: 1. (n – 2) 180 x = ________ 2. x = ________ 123˚ 134˚ 67˚ x˚x˚ 112˚ 87˚ 151˚ 75˚ x˚x˚

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

Missing EXTERIOR Angles **The SUM of the EXTERIOR angles in ALL polygons is 360˚ 8 *How to find a MISSING EXTERIOR ANGLE: EXAMPLE 1: EXAMPLE 2: 75˚ 142˚ x˚x˚ X = 360˚ 120˚ 85˚ 115˚ x˚x˚ X = 360˚

EXTERIOR ANGLES PRACTICE Solve for X: 87˚ 42˚ 35˚ 79˚ 24˚ x˚x˚

EXTERIOR ANGLES PRACTICE Find the missing exterior angle of a pentagon with four angles of 42˚, 56˚, 73˚, 100˚:

EXTERIOR ANGLES PRACTICE Solve for X: 52˚ x˚x˚

EXTERIOR ANGLES PRACTICE Solve for all missing angles: 40˚ A˚A˚ B˚B˚ C˚C˚D˚D˚ A = ____ B = ____ C = ____ D = _______

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

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

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 ÷ 2Diameter ( 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 ______ 10

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

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

CIRCLES: Pi ( Π) and Circumference 11 Circumference: The distance measure around an entire circle. Pi also known as Π = about 3.14 FORMULA for finding Circumference of any circle: C = Πdor C = 2Πr 7 in 2 cm

Finding Circumference C = 2Πr orC = Πd 3.5 in

Finding Circumference C = 2Πr orC = Πd 7.8 in

Finding Circumference C = 2Πr orC = Πd cm

Finding Circumference C = 2Πr orC = Πd 13.7 ft

Finding Circumference C = 2Πr orC = Πd 4.2 in

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

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

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

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