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Warm Up 1. Draw AB and AC , where A , B , and C are noncollinear.

Warm Up 1. Draw AB and AC , where A , B , and C are noncollinear. 2. Draw opposite rays DE and DF. Solve each equation. 3. 2 x + 3 + x – 4 + 3 x – 5 = 180 4. 5 x + 2 = 8 x – 10. B. A. C. D. E. F. Possible answer:. 31. 4. 11. 5 11/12 27. skip

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Warm Up 1. Draw AB and AC , where A , B , and C are noncollinear.

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  1. Warm Up • 1. Draw AB and AC, where A, B, and C are noncollinear. • 2. Draw opposite rays DE and DF. • Solve each equation. • 3. 2x + 3 + x – 4 + 3x – 5 = 180 • 4.5x + 2 = 8x – 10 B A C D E F Possible answer: 31 4

  2. 11. 5 11/12 27. skip 12. 3 ¼ 28. 60 cm, 12 cm 13. Skip 31. 3.375 14. 9.1 32. 4 15. 5 33. 9 16. 28 yd 34. 3 pts noncollinear 17. DE = EF = 14; DF = 28 35. skip 18. y = 7, QR = 21 36. D 50. AB, BC 19. midpt, 16 37. J 51. AD, BD 20. 9 1/3 38. B 52. A, B, D 21. 7.1 39. H 53. CB 22. 4.25 40. 26 23. 4 41. X A D N 24. A 43. 14.02 m 25. S 48. 5a – 22 26. A 49. - 8x + 6

  3. Angle: Vertex: Interior of Angle: Exterior of Angle: Naming Angles: Figure formed by 2 rays, or sides, with common endpoint common endpoint Set of all pts. between the sides of the angle Set of all pts. outside the angle S 1 R T Can be named with one letter, 3 letters or by number R SRT TRS 1 When figure has multiple angles, use 3 letters to identify

  4. Measure: Usually given in degrees

  5. Example 1 Use the diagram to find the measure of each angle. Then classify each as acute, right, or obtuse. a. BOA b. DOB c. EOC mBOA = 40° BOA is acute. mDOB = 125° DOB is obtuse. mEOC = 105° EOC is obtuse.

  6. Congruent Angles: Angles that have same measure Arc marks are used to show that the two angles are congruent. mXWZ = 121° and mXWY = 59°. Find mYWZ. Example 2 mYWZ = mXWZ – mXWY mYWZ= 121– 59 mYWZ= 62

  7. JK bisects LJM; thus LJKKJM. QS bisects PQR, mPQS = (5y – 1)°, and mPQR = (8y + 12)°. Find mPQS. Angle Bisector: Ray that divides angle into two congruent angles Example 3 mPQS = 5y – 1 5y – 1 = 4y + 6 = 5(7) – 1 y – 1 = 6 = 34 y = 7 Pg. 25 ______________________________________

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