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angle pairs.ppt
- 1. Angles Pairs
- 2. To denote the measure of an angle we write an “m” in front of the symbol for the angle. Here are some common angles and their measurements. 2 1 2 3 4 1 45 m 2 90 m 3 135 m 4 180 m Review
- 3. Congruent Angles • So, two angles are congruent if and only if they have the same measure. • So, The angles below are congruent. 3 if and only if . A B m A m B Means Congruent Means Equal Review
- 4. Perpendicular Lines •Two lines are perpendicular if they intersect to form a right angle. See the diagram. •Suppose 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. •So, perpendicular lines intersect to form four right angles. 4 1 2 3 4
- 5. Perpendicular Lines •The symbol for perpendicularity is •So, if lines m and n are perpendicular, then we write . . m n m n m n
- 6. Adjacent Angles Adjacent angles share a common vertex and one common side. Adjacent angles are “side by side” and share a common ray. 45º 15º
- 7. Adjacent Angles These are examples of adjacent angles. 55º 35º 50º 130º 80º 45º 85º 20º
- 8. Adjacent Angles These angles are NOT adjacent. 45º 55º 50º 100º 35º 35º
- 9. Vertical Angles •Two angles formed by intersecting lines and have no sides in common but share a common vertex. •Are congruent. When 2 lines intersect, they make vertical angles. 75º 75º 105º 105º Commo nVertex
- 12. Vertical angles are congruent (equal). 30º 150º 150º 30º Vertical Angles
- 13. Vertical Angles 1 4 Two angles that are opposite angles. Vertical angles are congruent. 1 2 3 4 5 6 7 8 2 3 5 8, 6 7 Name the Vertical Angles
- 14. Supplementary Angles Add up to 180º. 60º 120º 40º 140º Adjacent and Supplementary Angles
- 15. Supplementary Angles • Two angles are supplementary if their measures add up to • If two angles are supplementary each angle is the supplement of the other. • If two adjacent angles together form a straight angle as below, then they are supplementary. 15 180 . 1 2 1 and 2 are supplementary
- 16. Complementary Angles Add up to 90º. 70º 20º 20º 70º Adjacent and Complementary Angles
- 17. Complementary Angles • Two angles are if their measures add upcomplementary to • If two angles are complementary, then each angle is called the complement of the other. • If two adjacent angles together form a right angle as below, then they are complementary. 17 90 . 1 2 A B C 1 and 2 are complementary if is a right angle ABC
- 18. Supplementary vs. Complementary How do I remember? The way I remember is this: • C comes before S in the alphabet. • 90 comes before 180 when I count. • Complementary is 90, Supplementary is 180.
- 19. GuessWho? • 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? • I am two adjacent angles.
- 24. GuessWho? • I am two adjacent angles. • I look like an “L” with a line in the middle.
- 25. GuessWho? • I am two adjacent angles. • I look like an “L” with a line in the middle. • I add up to 90° • I look like this:
- 26. GuessWho? • I am two adjacent angles. • I look like an “L” with a line in the middle. • I add up to 90° • I look like this: Complementary Supplementary
- 29. Review • Complementary angles are…….
- 32. Practice Time!
- 33. Find the missing angle 55 x I know that these angles are complementary. They must add up to 90° So…… 90 – 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 – 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. So….. 180 – 120 = 60 The missing angle is 60
- 38. Find the missing angle 130 x What kind of angles? What’s the missing angle?
- 39. Find the missing angle 130 x What kind of angles? Supplementary What’s the missing angle? Adds up to 180, so….. 180 – 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 60º 120º
- 44. #2 60º 30º
- 46. #3 75º 75º
- 48. #4 60º 40º
- 49. #4 60º 40º None of the above
- 50. #5 60º 60º
- 52. #6 45º 135º
- 54. #7 65º 25º
- 56. #8 50º 90º
- 57. #8 50º 90º None of the above
- 58. Directions: Determine the missing angle.
- 59. #1 45º ?º
- 60. #1 45º 135º
- 61. #2 65º ?º
- 62. #2 65º 25º
- 63. #3 35º ?º
- 64. #3 35º 35º
- 65. #4 50º ?º
- 66. #4 50º 130º
- 67. #5 140º ?º
- 68. #5 140º 140º
- 69. #6 40º ?º
- 70. #6 40º 50º
- 71. ACTIVITY 1: LET’S PRACTICE! Direction:WriteTrue if the statement is correct but if it’s 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.