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Ms. King’s Little Book of Geometry Notes

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

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Ms. King’s Little Book of Geometry Notes

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  1. Ms. King’s Little Bookof Geometry Notes Period ___

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

  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 1.

  5. TYPE OF ANGLES Name the type of angle shown: 142˚

  6. TYPE OF ANGLES Name the type of angle shown: 27˚

  7. TYPE OF ANGLES Name the type of angle shown:

  8. TYPE OF ANGLES Name the type of angle shown: 180˚

  9. TYPE OF ANGLES Name the type of angle shown: What does angle x equal? x˚ 71˚

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

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

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

  13. 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°

  14. Ms. King’s Little Bookof Geometry Notes Period ___

  15. 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

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

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

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

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

  20. Interior Angle Sum Theorem 6

  21. 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

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

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

  24. 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˚

  25. Ms. King’s Little Bookof Geometry Notes Period ___

  26. 8 Missing EXTERIOR Angles **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˚

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

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

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

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

  31. Ms. King’s Little Bookof Geometry Notes Period ___

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

  33. 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 ______

  34. Ms. King’s Little Bookof Geometry Notes Period ___

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

  36. 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

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

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

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

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

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

  42. Finding Circumference C = 2Πr or C = Πd The Circumferenceof the circle is 21.98 cm. a) What is the diameter? b) What is the radius? d = ?

  43. Ms. King’s Little Bookof Geometry Notes Period ___

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

  45. 12 CIRCLES: Area Area: How much space the circle takesup (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

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