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Geometry

Geometry. Chapter 1 Section 6 Angles. Rays. A Ray has one endpoint and goes forever in one direction A Ray is named with the endpoint and one point on the ray. The Ray. A. B. Is called Ray BA never Ray AB. Name The Ray. R. G. Angle. 2 rays with a common endpoint

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Geometry

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  1. Geometry Chapter 1 Section 6 Angles

  2. Rays • A Ray has one endpoint and goes forever in one direction • A Ray is named with the endpoint and one point on the ray

  3. The Ray A B Is called Ray BA never Ray AB

  4. Name The Ray R G

  5. Angle • 2 rays with a common endpoint • The common endpoint is called the Vertex • The rays are called Sides Side Vertex Side

  6. Name an angle G T B With the angle Sign L and: • The vertex • A Point on one side, the vertex and a point on the other • A number designator • L G • L TGB • L 1 1

  7. Interior and exterior of an angle Interior Exterior

  8. 3 Letter Angle Name • A 3 letter angle name must be used if more than one angle shares a vertex T R F S If you named an angle L R Would you refer to L TRF , L TRS or L SRF?

  9. To Read an angle name • Pick the first letter is on a side, the middle letter is the vertex, and the third letter is on the other side L BTG G B T V C E Z

  10. To Read an angle name • LBTZ • L BTG • LCVE • LEVT • LZTV • LGTV • LBTV • LZTG G B T V C E Z

  11. Angle Measurement • Angles are measured in degrees • All Angles have measurements between 0 and 1800 The restrictions on an angle are 00 ≤ any angle ≤ 1800

  12. Special angles • An angle of measure 00 is a ray • An Angle of measure 1800 is called a Straight Angle • A Straight Angle is formed by Opposite Rays • An angle with a measure of 900is called a Right Angle

  13. Angle Congruence If 2 angles have the same measure then they are congruent If L Q @L R then m L Q =m L R Q R

  14. Angle Addition Postulate If R is on the interior of angle PQS Then m L PQR + m L RQS = m L PQS P Q R S

  15. Angle Addition Postulate • L GFE = 3x + 7 • L DFG = 4x + 20 • L EFD = 5x + 3 find x find L DFG G F E D

  16. Classifying Angles

  17. Restrictions on an Angle • If L NHM is Obtuse then 900 < L NHM < 1800 • If L KJW is Acute then 00 < L NHM < 900

  18. Restrictions on an Angle • If L NHM is Obtuse and L NHM = 2x+4 then find the restrictions on x 900 < L NHM < 1800 90 < 2x+4 < 180 86 < 2x < 176 43 < x < 88

  19. Restrictions on an Angle If L DRW is Obtuse and L DRW = 3x + 9 find the restrictions on x ___0 < L DRW < ___0

  20. Angle Bisector An Angle Bisector is a Ray that divides an angle into 2 @ angles G If L GFE @L EFD then FE is an angle bisector of L GFD F E D

  21. Angle Bisector • If FE is an angle bisector of L GFD and • L GFD = 5x -3 • L GFD = 2x +12 Find L EFD G F E D

  22. Do Now • Page 49 - 51 • Problems • 10 – 12 • 17 – 28 • 33 – 39 • 42 - 49

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