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

Essential Question “Our Goal” Can I classify angles? SPI: 0606.4.4

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

Essential Question: Can I classify angles? SPI: 0606.4.4 ACUTE Less than 90˚ 1.

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˚

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˚

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˚

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

TYPE OF ANGLES Name the type of angle shown: 37˚ x˚ 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: x˚ 152˚ What does angle x equal?

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°

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: 0606.4.2

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

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

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

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

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˚) 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

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

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

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

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

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˚

EXTERIOR ANGLES PRACTICE Solve for X: 35˚ 42˚ 79˚ 87˚ 24˚ 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: x˚ 52˚

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

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

ESSENTIAL QUESTION: “OUR GOAL” How do you calculate with circumferences and areas of circles?  (SPI: 0606.4.4)

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 ______

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

ESSENTIAL QUESTION: “OUR GOAL” How do you calculate with circumferences and areas of circles?  (SPI: 0606.4.4)

CIRCLES: Pi (Π) and Circumference 11 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

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

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

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

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

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

Finding Circumference C = 2Πr or C = Πd The Circumference of the circle is 21.98 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: 0606.4.4)

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

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

ESSENTIAL QUESTION: “OUR GOAL” How can you determine the surface area and volume of prisms, pyramids, and cylinders?  (SPI: 0606.4.5)

Surface Area: CYLINDER 13 *The area of a 3-dimensial object *Cylinder: 2 circular bases, and a rectangle. **FORMULA: (2Πr2) + (2Πr • h) 3 cm 7 cm