Geometry 

 

Transitive Property: If two things = the same thing, then they are equal to each other.

Addition Property: If you add the same thing to two equal things, then the results are equal.

Subtraction Property: If you subtract the same thing from two equal things, then your results are equal.

Multiplication Property: If you multiply the same things times two things, then the results are equal.

Division Property: If you divide the same thing into two equal things, then the results are equal.

Substitution Property: Equals may be substituted for equals.

Reflexive Property: Anything equals itself.

Symmetric Property: If A=B then B=A

Distributive Property: a(b+c) = ab + ac or combining like terms

 

If-Then Statements (Conditionals)

  1. If angles (segments) have equal measures, then they are congruent.
  2. If angles (segments) are congruent, then they have = measures.
  3. If a line and a ray form adjacent angles then they are supplementary.
  4. If a line and a ray form adjacent angles, then they form a linear pair.
  5. If two angles form a linear pair, then they are supplementary.
  6. If two angles are supplementary, then their sum is 180 degrees.
  7. If two angles add up to 180 degrees, then they are supplementary.
  8. If a segment has a midpoint, then it is divided into 2 congruent (equal) parts.
  9. If a segment is divided into 2 congruent (equal) parts, then it has a midpoint.
  10. If a ray bisects an angle, then it is divided into 2 congruent (equal) angles.
  11. If a ray divides an angle into 2 congruent (equal) parts, then it is a bisector.
  12. If the sum of two angles is 90 degrees, then they are complementary.
  13. If two angles are complementary, then their sum is 90 degrees.
  14. If 2 angles are vertical angles, then they are congruent.
  15. If 2 lines are perpendicular, then they form right angles.
  16. If two lines form right angles, then they are perpendicular.
  17. If two lines are perpendicular, then they form 4 right angles.
  18. If an angle is a right angle, then their measure is 90 degrees.
  19. If an angle measures 90 degrees, then it is a right angle.
  20. If 2 lines form = adjacent angles, then they are perpendicular.
  21. If two lines are perpendicular, then they form = adjacent angles.
  22. If two lines intersect to form one right angle, then they form four right angles.
  23. If one angle of a linear pair is a right angle, then the other angle is a right angle also.
  24. If angles are right angles, then they are congruent.
  25. If angles are supplementary to congruent angles, then they are congruent also.
  26. If angles are supplementary to the same angle, then they are congruent.
  27. If angles are complementary to congruent angles, then they are congruent also.
  28. If angles are complementary to the same angle, then they are congruent.

    29.  

  29. If parallel lines are intersected by a transversal, then alternate interior angles are congruent.
  30. If parallel lines are intersected by a transversal, then corresponding angles are congruent.
  31. If parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are supplementary.
  32. If alternate interior angles are congruent, then they form parallel lines.
  33. If corresponding angles are congruent, then they form parallel lines.
  34. If interior angles on the same side of the transversal are supplementary, then they form parallel lines.
  35. If two coplanar lines are perpendicular to the same line then they are parallel.
  36. If two lines are parallel to the same line, then they are parallel.
  37. If there is a triangle, then the sum of the measures of its angles is 180 degrees.
  38. If two angles of a triangle are congruent to two angles of another triangle, then the third angles are congruent.
  39. If the triangle ahs an exterior angle, then the exterior angle equals the sum of the remote interior angles.
  40. If a triangle is isosceles, then it has two sides congruent.
  41. If a triangle has two sides congruent, then it is isosceles.
  42. If two sides of a triangle are congruent, then the opposite angles are congruent.
  43. If two angles of a triangle are congruent, then the opposite sides are congruent.
  44. If a triangle is equilateral, then it has three equal sides.
  45. If a triangle has three equal sides, then it is equilateral.
  46. If a triangle is equilateral, then each angle equals 60 degrees.
  47. If a triangle is equilateral, then it is equiangular.
  48. If a triangle is equiangular, then it is equilateral.
  49. Triangles can be proven congruent by:

    50. SAS for congruent triangles

    ASA for congruent triangles

    SSS for congruent triangles

    AAS for congruent triangles

    [No donkeys (ASS) or towtrucks (AAA)]

  50. (CPCTC) Corresponding Parts of Congruent Triangles are Congruent
  51. Right Triangles can be proven congruent by:                       HL for right triangles

    52.                         Or

                    HA for right triangles

52. If a triangle has a right angle, then it is a right           triangle.