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7-1 7-2 Angles PA

7-1 7-2 Angles PA. Measurement of an Angle. 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. 1. 2. 4. 3. Congruent Angles.

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7-1 7-2 Angles PA

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  1. 7-1 7-2 Angles PA

  2. Measurement of an Angle

  3. 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. 1 2 4 3

  4. Congruent Angles • So, two angles are congruent if and only if they have the same measure. • So, The angles below are congruent. Means Congruent Means Equal

  5. Types of Angles • An acuteangle is an angle that measures less than 90 degrees. • A rightangle is an angle that measures exactly 90 degrees. • An obtuseangle is an angle that measures more than 90 degrees. right obtuse acute

  6. Types of Angles • A straightangle is an angle that measures 180 degrees. (It is the same as a line.) • When drawing a right angle we often mark its opening as in the picture below. right angle straight angle

  7. 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. 2 1 4 3

  8. Perpendicular Lines • The symbol for perpendicularity is • So, if lines m and n are perpendicular, then we write m n

  9. Adjacent Angles Adjacent angles share a common vertex and one common side. Adjacent angles are “side by side” and share a common ray. Common Ray 15º 45º Common Vertex

  10. Adjacent Angles These are examples of adjacent angles. 45º 80º 35º 55º 130º 50º 85º 20º

  11. Adjacent Angles These angles are NOT adjacent. 100º 50º 35º 35º 55º 45º

  12. Vertical Angles • Two angles formed by intersecting lines and have no sides in common but share a common vertex. • Are congruent. Common Vertex 75º When 2 lines intersect, they make vertical angles. 105º 105º 75º

  13. Vertical Angles Vertical angles are opposite one another. 75º 105º 105º 75º

  14. Vertical Angles Vertical angles are opposite one another. 75º 105º 105º 75º

  15. Vertical Angles Vertical angles are congruent (equal). 150º 30º 150º 30º

  16. Vertical Angles Two angles that are opposite angles. Vertical angles are congruent. Name the Vertical Angles 1  4  5  8, 1 2 6  7  2  3 3 4 5 6 7 8

  17. Supplementary Angles Add up to 180º. 40º 120º 60º 140º Supplementary Anglesbut not Adjacent Adjacent and Supplementary Angles

  18. Supplementary Angles • Two angles are supplementary if their measures add up to • If two angles are supplementary each angle is the supplementof the other. • If two adjacent angles together form a straight angle as below, then they are supplementary. 1 2

  19. Complementary Angles Add up to 90º. 20º 20º 70º 70º Complementary Anglesbut not Adjacent Adjacent and Complementary Angles

  20. A C B Complementary Angles • Two angles are if their measures add upcomplementary to • If two angles are complementary, then each angle is called the complementof the other. • If two adjacent angles together form a right angle as below, then they are complementary. 1 2

  21. Supplementary vs. ComplementaryHow 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.

  22. Guess Who? • I am an angle.

  23. Guess Who? • I am an angle. • I have 180°

  24. Guess Who? • I am an angle. • I have 180° • I look like this:

  25. Guess Who? • I am an angle. • I have 180° • I look like this: Supplementary Complementary

  26. Guess Who? • I am two adjacent angles.

  27. Guess Who? • I am two adjacent angles. • I look like an “L” with a line in the middle.

  28. Guess Who? • 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:

  29. Guess Who? • 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

  30. Guess Who? Complementary Supplementary

  31. Guess Who? Complementary Supplementary

  32. Review • Complementary angles are…….

  33. Review • Complementary angles are…….

  34. Review • Supplementary Angles are…..

  35. Practice Time!

  36. Find the missing angle I know that these angles are complementary. They must add up to 90° So…… 90 – 55 = 35 The missing angle is 35 55 x

  37. You try. Are they supplementary or complementary? Find the missing side. x 20

  38. You try. Are they supplementary or complementary? complementary Find the missing side. 90 – 20 = 70 The missing angle Is 70 x 20

  39. One More 50 x

  40. 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

  41. Find the missing angle 130 x What kind of angles? What’s the missing angle?

  42. Find the missing angle 130 x What kind of angles? Supplementary What’s the missing angle? Adds up to 180, so….. 180 – 130 = 50

  43. Find the missing angle x 30 Do this one on your own.

  44. Directions: Identify each pair of angles as adjacent, vertical, supplementary, complementary, or none of the above.

  45. #1 120º 60º

  46. #1 120º 60º Supplementary Angles Adjacent Angles

  47. #2 60º 30º

  48. #2 60º 30º Complementary Angles

  49. #3 75º 75º

  50. #3 Vertical Angles 75º 75º

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