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Definitions, Postulates, Theorems, and Corollaries First Semester Geometry Chapter 1 1. Equidistant 2. Point 3. Line 4. Plane 5. Space 6. Collinear 7. Non-collinear 8. Coplanar 9. Non-coplanar 10. Intersect 11. Intersection 12. Segment 13. Ray 14. Opposite rays 15. Coordinate of a point 16. Length of a segment 17. Postulate 18. Ruler Postulate (Postulate 1) 19. Segment Addition Postulate (Postulate 2) 20. Congruent (≅) 21. Congruent (≅) segments Chapter 2 1. If-then statements ⇒ conditional statements 2. Hypothesis 3. Conclusion 4. Converse 5. Counterexample 6. If and only if statements ⇒ biconditional statements 7. Addition Property of equality 8. Subtraction Property of equality 9. Multiplication Property of equality 10. Division Property of equality 11. Substitution of equality 12. Reflexive of equality 13. Symmetric of equality 14. Transitive of equality 15. Reflexive Property of congruence 16. Symmetric Property of congruence 17. Transitive Property of congruence 18. Distributive Chapter 3 1. Intersecting lines 2. Non-Intersecting lines 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. Midpoint of a segment (Midpt) Bisector of a segment Angle Sides Vertex Acute angle Right angle Obtuse angle Straight angle Angle Addition Postulate (Postulate 4) – 2 Parts Congruent angles Adjacent angles Angle bisector Postulate 5 Postulate 6 Postulate 7 Postulate 8 Postulate 9 Theorem 1-1 Theorem 1-2 Theorem 1-3 Theorem 2-1 : Midpoint Theorem Theorem 2-2 : Angle Bisector Theorem Reasons We Can Use in a Proof: a. Given Information b. Definitions c. Postulates (including algebra properties) d. Proven theorems e. Corollaries Complementary angles (complements) Supplementary angles (supplements) Vertical angles Theorem 2-3 Perpendicular Lines ( ⊥ ) Theorem 2-4 Theorem 2-5 Theorem 2-6 Theorem 2-7 Theorem 2-8 3. Parallel lines ( 4. Skew lines ) First Semester Postulates, Theorems, Corollaries and Definition – Page 1 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. Parallel planes Definition of a line parallel to a plane Theorem 3-1 Transversal Alternate interior angles (alt. int) Alternate exterior angles (alt. ext) Same-Side Interior (s-s int) Same-side Exterior (s-s ext) Corresponding (corr.) Postulate 10 Theorem 3-2 Theorem 3-3 Theorem 3-4 Postulate 11 Theorem 3-5 Theorem 3-6 Theorem 3-7 Theorem 3-8 Theorem 3-9 Theorem 3-10 Auxiliary Lines Triangle Vertex (vertices) Sides of a ∆ Scalene Triangle Isosceles Triangle Equilateral Triangle Equiangular Triangle Chapter 4 1. Congruent Polygons 2. CPCTC 3. Regular polygons 4. Common Side 5. Postulate 12 – SSS Post 6. Postulate 13 – SAS Post 7. Postulate 14 – ASA Post 8. Theorem 4-3 – AAS 9. Definition of a Line perpendicular to a plane 10. Isosceles Triangle 11. Legs of an Isosceles Triangle 12. Base of an Isosceles Triangle 13. Base Angles of an Isosceles Triangle 14. Vertex angle of an Isosceles Triangle 15. Theorem 4-1 – Isosceles Triangle Theorem 16. Corollary 1 to Theorem 4-1 17. Corollary 2 to Theorem 4-1 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. 50. 51. 52. 53. 54. 55. 56. 57. 58. 59. 60. Acute Triangle Obtuse Triangle Right Triangle Theorem 3-11 Corollary 1 to Theorem 3-11 Corollary 2 to Theorem 3-11 Corollary 3 to Theorem 3-11 Corollary 4 to Theorem 3-11 Exterior angles of a triangle Remote interior angles of a triangle Theorem 3-12 Polygon Convex polygon Concave polygon Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Diagonals of a polygon Theorem 3-13 Theorem 3-14 Equiangular Polygon Equilateral Polygon Regular polygon 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. Corollary 3 to Theorem 4-1 Theorem 4-2 Corollary to Theorem 4-2 Overlapping Triangles Right Triangle Hypotenuse Theorem 4-4 – HL Theorem LL Theorem HA Theorem LA Theorem Median of a Triangle Altitude of a Triangle Perpendicular Bisector Theorem 4-5 Theorem 4-6 Definition of the Distance from a point to a line Theorem 4-7 Theorem 4-8 34. 35. First Semester Postulates, Theorems, Corollaries and Definition – Page 2