Geometry proofs vocab.

**PROOF LIST (LIVE DOCUMENT) TO STUDY**

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| **⇔** | **Bi-Conditional “… if and only if …”** |
|----|----|
| **⇒** | **Implies “if… , then…”** |
| **∠** | **Angle** |
| **m∠** | **Measure of Angle** |
| **≌** | **Congruent** |
| **∥** | **Parallel** |
| **⊥** | **Perpendicular** |

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| Addition Property of Equality | If *a* = *b*, then *a* + *c* = *b* + *c* |
|----|----|
| Subtraction Property of Equality | If *a* = *b*, then *a* – *c* = *b* – *c* |
| Multiplication Property of Equality | If *a* = *b*, then *ac* = *bc* |
| Division Property of Equality | If *a* = *b* and *c* ≠ 0, then |
| Substitution Property of Equality | If *a* = *b*, then *a* can be substituted for *b* in any equation or expression. |
| Distributive Property | *a* ( *b* + *c* ) = *ab* + *ac*, where *a*, *b*, and *c*, are real numbers |
| Simplify | Combine like terms |
| Reflexive Property of Equality | a = a,   AB = AB, m∠ *A* = m∠ *A* |
| Reflexive Property of Congruence |  ∠ *A* ≅ ∠ *A* |
| Symmetric Property of Equality  | If a = b, then b = a , If *AB* = *CD*, then *CD* = *AB,*         If *m*∠*A* = *m*∠ *B*, then *m*∠ *B* = *m*∠ *A* |
| Symmetric Property of Congruence | If , thenIf ∠ *A* ≅ ∠ *B*, then ∠ *B* ≅ ∠ *A* |
| Transitive Property of Equality  | If a = b and b = c, then a = c,If *AB* = *CD* and *CD* = *EF*, then *AB* = *EF,*If *m*∠ *A* = *m*∠ *B* and *m*∠ *B* = *m*∠ *C*, then *m*∠ *A* = *m*∠ *C* |
| Transitive Property of Congruence | If a = b  and b = c , then a = c.If ∠ *A* ≅ ∠ *B* and ∠ *B* ≅ ∠ *C*, then ∠ *A* ≅ ∠ *C* |
| Substitution Property | If a = b, then a can be substituted for b. |

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**__Definitions__**

Congruent  - also equal in measure

Angle Bisector  - divides into two ≅ angle

Segment bisector - line, segment or ray that divides a segment at the midpoint

Midpoint – a point that divides a line segment into two ≅ segments

Supplementary angles - two angles that add up to 180˚

Complementary Angles - two angles that add up to 90˚

Linear Pair – pair of angles that are adjacent and supplementary

Right Angle – Angle measures exactly 90˚

Perpendicular - intersects at a right angle, creates a right angle

Vertical Angles - if vertical angles, then they are congruent

**__Postulates (assumed true without proof)__**

Segment Addition Postulate – If B is between AC on a line segment, then AB + BC = AC

Angle Addition Postulate – If T is in the interior of ∠ABC, then m∠ABT + m∠TBC = m∠ABC

Right Angle Congruence – all right angles are congruent

**__Theorems (statements that have been proven)__**

Congruent Complements Theorem - two angles complementary to the same angle or congruent angles are congruent

Congruent Supplements Theorem - two angles supplementary to the same angle or congruent angles are congruent

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