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Geometric Theorems and Angle Relationships Explained

Learn about the Segment Addition Postulate, Midpoint Theorem, Angle Bisector Theorem, and more in geometry with clear explanations and examples. Enhance your understanding of angles and line relationships.

kaseem-richard
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Geometric Theorems and Angle Relationships Explained

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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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