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Angle Measure

Angle Measure. Sec: 1.4 Sol : G.4d,e. Ray. Is Part of a line Has one endpoint and extends indefinitely in one direction. Named by stating the endpoint and any other point on the ray. (endpoint must be stated first.) Denoted with an arrow pointing in one direction. AB. Example.

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Angle Measure

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  1. Angle Measure Sec: 1.4 Sol: G.4d,e

  2. Ray • Is Part of a line • Has one endpoint and extends indefinitely in one direction. • Named by stating the endpoint and any other point on the ray. (endpoint must be stated first.) Denoted with an arrow pointing in one direction. AB

  3. Example Named: Or Note: E has to go first!!! G F E

  4. Opposite Rays • Two rays that fall on the same line, but go in opposite directions. are opposite rays. They are also collinear rays. Q P R

  5. Angles • Are formed By two non-collinear rays. • They have a common endpoint. • The two rays are called sides of an angle. • The common endpoint is the vertex. Side B Vertex A C Side

  6. There are three ways to name an angle Using 3 points: The vertex must be the middle letter This angle can be named as Using 1 point: using only vertex letter (only used when there is only one angle present). Since B is the vertex of only this angle, this can also be called . A C B Lesson 1-4: Angles

  7. Naming an Angle - continued Using a number: when naming with a number you use the number on the interior of the angle. A B 2 C * The “1 letter” name is unacceptable when … more than one angle has the same vertex point. In this case, use the three letter name or a number if it is present. Lesson 1-4: Angles

  8. Angles Continued • Name the following angle. B A 4 C

  9. Example • K is the vertex of more than one angle. Therefore, there is NO in this diagram. There is Lesson 1-4: Angles

  10. Angle and Points • Angles can have points in the interior, in the exterior or on the angle. E A D B C Points A, B and C are on the angle. D is in the interior and E is in the exterior. B is the vertex. Lesson 1-4: Angles

  11. Example Name all angles with B as a vertex. 2. Name the sides of <5. 3. Write another name for <6.

  12. Classifying Angles: D A B C

  13. Example Classify each angle as right, obtuse, acute or straight. 1. <TYV 2. < WYT 3. <TYU 4. <TYX

  14. Congruent angles • Two angles with the same angle measure (Note: Arcs on the angle signify that they are congruent.) Example:

  15. Angle Addition Postulate Postulate: The sum of the two smaller angles will always equal the measure of the larger angle. Complete: m  ____ + m ____ = m  _____ MRK KRW MRW Lesson 1-4: Angles

  16. Adding Angles m1 + m2 = mADC also. Therefore, mADC = 58. Lesson 1-4: Angles

  17. Example: Angle Addition K is interior to MRW, m  MRK = (3x), m KRW = (x + 6) and mMRW = 90º. Find mMRK. First, draw it! 3x + x + 6 = 90 4x + 6 = 90 – 6 = –6 4x = 84 x = 21 3x x+6 Are we done? mMRK = 3x = 3•21 = 63º Lesson 1-4: Angles

  18. Example: Angle Addition K is interior to MRW, m  MRK = (2x + 10), m KRW = (4x - 3) and mMRW = 145º. Find mMRK and m KRW. First, draw it! 2x + 10 How can you check this? 4x - 3 Lesson 1-4: Angles

  19. Angle Bisectors • Is a ray that divides an angle into two congruent halves. • bisects RPS, m RPQ = 3x+6°and the m∠QPS =4x-8° . Find m RPS. m RPS = m RPQ + m QPS

  20. Assignments Classwork: Handout Homework: Handout

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