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angle pairs.ppt
- 1. Angles Pairs
- 2. To denote the measure of an angle we write an âmâ in front of the symbol for the angle. Here are some common angles and their measurements. 2 1 2 3 4 1 45 mï ïœ ï° 2 90 mï ïœ ï° 3 135 mï ïœ ï° 4 180 mï ïœ ï° Review
- 3. Congruent Angles âą So, two angles are congruent if and only if they have the same measure. âą So, The angles below are congruent. 3 if and only if . A B m A m B ï ï ï ï ïœ ï Means Congruent Means Equal Review
- 4. Perpendicular Lines âąTwo lines are perpendicular if they intersect to form a right angle. See the diagram. âąSuppose angle 2 is the right angle. Then since angles 1 and 2 are supplementary, angle 1 is a right angle too. Similarly, angles 3 and 4 are right angles. âąSo, perpendicular lines intersect to form four right angles. 4 1 2 3 4
- 5. Perpendicular Lines âąThe symbol for perpendicularity is âąSo, if lines m and n are perpendicular, then we write . ï . m n ï m n m n ï
- 6. Adjacent Angles Adjacent angles share a common vertex and one common side. Adjacent angles are âside by sideâ and share a common ray. 45Âș 15Âș
- 7. Adjacent Angles These are examples of adjacent angles. 55Âș 35Âș 50Âș 130Âș 80Âș 45Âș 85Âș 20Âș
- 8. Adjacent Angles These angles are NOT adjacent. 45Âș 55Âș 50Âș 100Âș 35Âș 35Âș
- 9. Vertical Angles âąTwo angles formed by intersecting lines and have no sides in common but share a common vertex. âąAre congruent. When 2 lines intersect, they make vertical angles. 75Âș 75Âș 105Âș 105Âș Commo nVertex
- 12. Vertical angles are congruent (equal). 30Âș 150Âș 150Âș 30Âș Vertical Angles
- 13. Vertical Angles ï 1 ï ï 4 Two angles that are opposite angles. Vertical angles are congruent. 1 2 3 4 5 6 7 8 ï 2 ï ï 3 ï 5 ï ï 8, ï 6 ï ï 7 Name the Vertical Angles
- 14. Supplementary Angles Add up to 180Âș. 60Âș 120Âș 40Âș 140Âș Adjacent and Supplementary Angles
- 15. Supplementary Angles âą Two angles are supplementary if their measures add up to âą If two angles are supplementary each angle is the supplement of the other. âą If two adjacent angles together form a straight angle as below, then they are supplementary. 15 180 . ï° 1 2 1 and 2 are supplementary ï ï
- 16. Complementary Angles Add up to 90Âș. 70Âș 20Âș 20Âș 70Âș Adjacent and Complementary Angles
- 17. Complementary Angles âą Two angles are if their measures add upcomplementary to âą If two angles are complementary, then each angle is called the complement of the other. âą If two adjacent angles together form a right angle as below, then they are complementary. 17 90 . ï° 1 2 A B C 1 and 2 are complementary if is a right angle ABC ï ï ï
- 18. Supplementary vs. Complementary How do I remember? The way I remember is this: âą C comes before S in the alphabet. âą 90 comes before 180 when I count. âą Complementary is 90, Supplementary is 180.
- 19. GuessWho? âą I am an angle.
- 20. GuessWho? ⹠I am an angle. ⹠I have 180°
- 21. GuessWho? ⹠I am an angle. ⹠I have 180° ⹠I look like this:
- 22. GuessWho? ⹠I am an angle. ⹠I have 180° ⹠I look like this: Supplementary Complementary
- 23. GuessWho? âą I am two adjacent angles.
- 24. GuessWho? âą I am two adjacent angles. âą I look like an âLâ with a line in the middle.
- 25. GuessWho? âą I am two adjacent angles. âą I look like an âLâ with a line in the middle. âą I add up to 90° âą I look like this:
- 26. GuessWho? âą I am two adjacent angles. âą I look like an âLâ with a line in the middle. âą I add up to 90° âą I look like this: Complementary Supplementary
- 29. Review âą Complementary angles areâŠâŠ.
- 32. Practice Time!
- 33. Find the missing angle 55 x I know that these angles are complementary. They must add up to 90° SoâŠâŠ 90 â 55 = 35 The missing angle is 35
- 34. You try. 20 x Are they supplementary or complementary? Find the missing side.
- 35. You try. 20 x Are they supplementary or complementary? complementary Find the missing side. 90 â 20 = 70 The missing angle Is 70
- 36. One More 50 x
- 37. Find the missing angle 120 x I know these are supplementary angles. Supplementary angles add up to 180. The given angle is 120. SoâŠ.. 180 â 120 = 60 The missing angle is 60
- 38. Find the missing angle 130 x What kind of angles? Whatâs the missing angle?
- 39. Find the missing angle 130 x What kind of angles? Supplementary Whatâs the missing angle? Adds up to 180, soâŠ.. 180 â 130 = 50
- 40. Find the missing angle x 30 Do this one on your own.
- 41. Directions: Identify each pair of angles as adjacent, vertical, supplementary, complementary, or none of the above.
- 42. #1 60Âș 120Âș
- 44. #2 60Âș 30Âș
- 46. #3 75Âș 75Âș
- 48. #4 60Âș 40Âș
- 49. #4 60Âș 40Âș None of the above
- 50. #5 60Âș 60Âș
- 52. #6 45Âș 135Âș
- 54. #7 65Âș 25Âș
- 56. #8 50Âș 90Âș
- 57. #8 50Âș 90Âș None of the above
- 58. Directions: Determine the missing angle.
- 59. #1 45Âș ?Âș
- 60. #1 45Âș 135Âș
- 61. #2 65Âș ?Âș
- 62. #2 65Âș 25Âș
- 63. #3 35Âș ?Âș
- 64. #3 35Âș 35Âș
- 65. #4 50Âș ?Âș
- 66. #4 50Âș 130Âș
- 67. #5 140Âș ?Âș
- 68. #5 140Âș 140Âș
- 69. #6 40Âș ?Âș
- 70. #6 40Âș 50Âș
- 71. ACTIVITY 1: LETâS PRACTICE! Direction:WriteTrue if the statement is correct but if itâs False, change the underlined word or number to make the whole statement true. __________1.Complementary angles measure 180 degree. __________2.The sum of the measures of angles at a point is 360 degree. __________3. If two angles form a linear pair, then they are complementary. __________4.The measures of adjacent angles are congruent. __________5. If the sum of two adjacent angles is 180degree, then these angles form a linear pair.
- 74. Valuing REFLECTION: (JournalWriting) Take a look around you.There are many things that works in pair. Give one example of it and compose a song pertaining to the importance of working by pair in real life.