Honors Geometry/Math 2 - Master List of All Properties
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12 terms
Terms | Definitions |
|---|---|
 Addition Property (Property of Equality) | If a = b and c = d, then a + c = b + d. |
| Subtraction Property (Property of Equality) | If a = b and c = d, then a - c = b - d. |
| Multiplication Property (Property of Equality) | If a = b, then ca = cb. |
| Division Property (Property of Equality) | If a = b and c does not equal 0, then a/c = b/c. |
| Substitution Property (Property of Equality) | If a = b, then either a or b may be substituted for the other in any equation. |
| Reflexive Property (Property of Equality) | a = a. |
| Symmetric Property (Property of Equality) | If a = b, then b = a. |
| Transitive Property (Property of Equality) | If a = b, and b = c, then a = c. |
| Reflexive Property (Property of Congruence) | AB ≡ AB, ∠A ≡ ∠A. |
| Symmetric Property (Property of Congruence) | If AB ≡ CD, then CD ≡ AB. If ∠A ≡ ∠B, then ∠B ≡ ∠A. |
| Transitive Property (Property of Congruence) | If AB ≡ CD, and CD ≡ DE, then AB ≡ DE. If ∠A ≡ ∠B, and ∠B ≡ ∠C, then ∠A ≡ ∠C. |
| A Property of Proportions (APOP) | 1. a/b is equivalent to the following: a. ad = bc (this is the one most used in proofs)* b. (a/c) = (b/d) c. (b/a) = (d/c) d. ((a + b)/b) = ((c + d)/d) 2. If (a/b) = (c/d) = (e/f)..., then (a + c + e + .../ b + d + f + ...). *This property is used because it is often necessary to replace a proportion with an equivalent proportion, especially in proofs. |
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