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GR + RE = GE

1. 6. 11. 16. 21. 2. 7. 12. 17. 22. 3. 8. 13. 18. 23. 4. 9. 14. 19. 24. 5. 10. 15. 20. 25. GR + RE = GE. Segment Addition Postulate. If R is the midpoint of GE, then RE = ½ GE. __. Midpoint Theorem. ↔. ↔. If RA  RD, then ARD is a right angle.

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GR + RE = GE

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  1. 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25

  2. GR + RE = GE

  3. Segment Addition Postulate

  4. If R is the midpoint of GE, then RE = ½ GE. __

  5. Midpoint Theorem

  6. ↔ ↔ If RA  RD, then ARD is a right angle.

  7. Def. of Perpendicular Lines

  8. If GRC is supplementary to ARC, and DRF is supplementary to ARC, then GRC  DRF.

  9. Congruent Supplements Theorem

  10. GRB  ERF

  11. Vertical Angles Are Congruent.

  12. → If RC bisects BRD, then mBRC = ½ mBRD.

  13. Angle Bisector Theorem

  14. mGRA + mARC = mGRC.

  15. Angle Addition Postulate

  16. ↔ ↔ If BF  GE, then GRB  BRE.

  17. If two lines are perpendicular, then they form congruent adjacent angles.

  18. If mERD + mCRA = 90, then those angles are complementary.

  19. Definition of Complementary Angles

  20. __ __ If BR  RF, then R is the midpoint of BF. __

  21. Definition of Midpoint

  22. → → If RB  RE, then BRC is complementary to CRE.

  23. If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary.

  24. If GRA is supplementary to FRD, then mGRA + mFRD = 180.

  25. Definition of Supplementary Angles

  26. __ If R is the midpoint of GE, then FB bisects GE. __ ↔

  27. Definition of Segment Bisector

  28. If BRE  ERF, then EG  FB. ↔ ↔

  29. If two lines form congruent adjacent angles, then the lines are perpendicular.

  30. mARB + mBRC = mARC

  31. Angle Addition Postulate

  32. __ __ If BR  RF, then R is the midpoint of BF. __

  33. Definition of Midpoint

  34. If mARD = 90, then ARD is a right angle.

  35. Definition of Right Angle

  36. If ARD is a right angle, then RA  RD. → →

  37. Definition of Perpendicular Lines

  38. ↔ ↔ If FB  GE, then BRE  ERF.

  39. If two lines are perpendicular, then they form congruent adjacent angles.

  40. If ARB is complementary to BRD, and DRE is complementary to BRD, then ARB  DRE.

  41. Congruent Complements Theorem

  42. → If RC bisects BRD, then BRC  CRD.

  43. Definition of Angle Bisector

  44. mGRC + mCRE = 180

  45. Linear Pair Postulate

  46. If BRG  BRE, then BR  GE. ↔ ↔

  47. If two lines form congruent adjacent angles, then the lines are perpendicular.

  48. FR + RB = FB

  49. Segment Addition Postulate

  50. → → If RB  RE, then BRD and DRE are complementary.

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