1 / 23

Geometry

Geometry. Lesson 1 – 5 Angle Relationships. Objective: Identify and use special pairs of angles. Identify perpendicular lines. Adjacent angles. 2 angles that lie in the same plane and have a common vertex and side, but no common interior points.

mpitcher
Download Presentation

Geometry

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Geometry Lesson 1 – 5 Angle Relationships Objective: Identify and use special pairs of angles. Identify perpendicular lines.

  2. Adjacent angles • 2 angles that lie in the same plane and have a common vertex and side, but no common interior points.

  3. Determine whether angles 1 and 2 are adjacent. No, angles do not share a vertex or side. No, do not share a common side Yes

  4. Determine whether angles 1 and 2 are adjacent. No, angles do not share a side. No, angles do not share a vertex.

  5. Determine whether angles 1 and 2 are adjacent. No, angles do not share a side. No, angles do not Share a vertex. Yes

  6. Determine whether the pair of angles are adjacent. A B Yes C E D No, can’t have one angle inside the other.

  7. Linear Pair • A pair of adjacent angles with noncommon sides that are opposite rays. • Linear pairs are supplementary

  8. Example • In the figure, CM and CE are opposite rays. • Name the angle that forms a linear pair with angle 1 • Do form a linear pair? Justify your answer. *Hint: what completes the 180 degrees or straight line No, they do not form a linear pair. The two angles do not add up to be 180 and do not create opposite rays.

  9. Your turn • Name the angle that forms a linear pair with • Tell whether form a linear pair. Justify your answer. Yes, they are adjacent and their noncommon sides are opposite rays.

  10. Your Turn • Name the angle that forms a linear pair with • Do form a liner pair? Justify your answer. No, they are not adjacent angles.

  11. Vertical Angles • Vertical angle: • Two angles are vertical if and only if they are two nonadjacent angles formed by a pair of interesting lines. 100 80 80 100

  12. Theorem • Vertical angle Theorem: • Vertical angles are congruent.

  13. Example • Find the value of x in each figure. 5x = 25 x = 130 (vertical) x = 5

  14. Complementary Angles • 2 angles with measures that have a sum of 90.

  15. Supplementary • Two angles with measures that have a sum of 180.

  16. Example • Find the measure of two supplementary angles if the difference in the measures of the two angles is 18. Let one angle be x and the other y. Write your equations. x – y = 18 99 + y = 180 y = 81 x + y = 180 + 2x = 198 x = 99

  17. Example • Find the measure of 2 complementary angles if the measure of the larger angle is 12 more than twice the measure of the smaller angle. Let x and y be the angles x = 12 + 2(26) = 64 x = 12 + 2y x + y = 90 (12 + 2y) + y = 90 3y + 12 = 90 3y = 78 y = 26

  18. Perpendicular Lines • Form 4 right angles • Form congruent adjacent angles • Segments and rays can be perpendicular • Right angle symbol shows perpendicular.

  19. Example 2x + 5x + 6 = 90 • Find x and y so that PR and SQ are perpendicular. 7x + 6 = 90 7x = 84 x = 12 4y – 2 = 90 4y = 92 y = 23

  20. Interpreting Diagrams • Are the lines perpendicular?

  21. Interpret • What can you assume? • What appears true, but cannot be assumed?

  22. Determine whether each statement can be assumed from the figure. Explain. • are complementary • are a linear pair. No, congruent but we don’t know if complementary Yes, adjacent angles whose noncommon sides are opposite rays Yes, they form a right angle which means they are perpendicular.

  23. Homework • Pg. 50 1 – 7 all, 8 – 44 EOE, 58 – 66 E

More Related