Algebraic Proofs

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  1. If a=b, then a+c=b+c
    Addition Property of Equality
  2. If a=b, then a-c=b-c
    Subtraction Property of Equality
  3. If a=b, then a*c=b*c
    Multiplication Property of Equality
  4. If a=b, then (a/c)=(b/c)
    Division Property of Equality
  5. a(b+c)=ab+ac

    Distributive Property of Multiplication over Addition

    Distributive Property of Multiplication over Subtraction
  6. If a=b, then b can be substituted for a in any equation or expression
    Substitution Property of Equality
  7. For any real number a, a=a
    Reflexive Property of Equality
  8. If a=b, then b=a
    Symmetric Property of Equality
  9. If a=b and b=c, then a=c
    Transitive Property of Equality
  10. For any geometric figure A, A is congruent to A
    Reflexive Property of Congruence
  11. If A is congruent to B, then B is congruent to A
    Symmetric Property of Congruence
  12. If A is congruent to B and B is congruent to C, then A is congruent to C
    Transitive Property of Congruence
  13. If C is between A and B, then AC+CB=AB
    Segment Addition Postulate
  14. If line segment  AB is congruent to line segment CB, then AB=CD
    Definition of Segment Congruence
  15. A geometric figure that divides a segment in to two congruent halves
    Definition of a segment bisector
  16. A point that bisects a segment
    Definition of a midpoint
  17. If C is on the interior of angle ABD, then the measure of angle ABC+ the measure of angle CBD equals the measure of angle ABD
    Angle Addition Postulate
  18. If angle A is congruent to angle B, Then the measure of angle A is equal to the measure of angle B
    Definition of Angle Congruence
  19. A geometric figure that divides an angle in to two congruent halves
    Definition of an Angle Bisector
  20. What are the four types of Congruence Theorems?
    • SSS
    • SAS
    • ASA
    • AAS
  21. When two lines are crossed by another line (which is called the Transversal), the angles in matching corners are called...
    Corresponding Angles

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  22. These are the angles opposite each other when two lines cross. They are always equal.
    Vertical Angles

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  23. Any of the four angles that do not include a region of the space between two lines intersected by a transversal.
    Exterior Angles

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  24. an angle formed between parallel lines by a third line that intersects them.
    Interior Angles

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  25. It is intended as an easy way to remember that when you have two triangles and you have proved they are congruent, then each part of one triangle (side, or angle) is congruent to the corresponding part in the other.
  26. What does this symbol mean?

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  27. What is line BD also known as?

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    an Angle Bisector

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Card Set
Algebraic Proofs
Geometry Test- Algebraic Proofs
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