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Geometry Proofs
| Term | Definition |
|---|---|
| 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, then a/c = b/c |
| Distributive Property | if a (b + c), then a (b + c) = ab + ac |
| Substitution Property | if a = b, then a maybe be replaced by b in any expression or equation |
| Reflexive Property | for any real number a, a = a (a value will always equal itself) |
| Symmetric Property | if a = b, then b = a |
| Transitive Property | if a = b and b = c, then a = c |
| Reflexive Property of Congruence | for any segment AB, AB is congruent to AB |
| Symmetric Property of Congruence | if AB is congruent to CD, then CD is congruent to AB |
| Transitive Property of Congruence | if AB is congruent to CD, and CD is congruent to EF, then AB is congruent to EF |
| Definition of Congruence (Segments) | Segments are congruent if and only if they have the same measure; if AB is congruent to CD, then AB = CD, and vice versa |
| Definition of Midpoint | Divides the segment into 2 equal (congruent) parts; if M is the ______________ of AB, then AM = MB |
| Segment Addition Postulate | if A, B, and C are collinear points and B is between A and C, then AB + BC = AC |
| Definition of Angle Bisector | an angle bisector divides an angle into two equal parts |
| Definition of Complementary Angles | sum of 90 degrees |
| Definition of Supplementary Angles | sum of 180 degrees |
| Definition of Perpendicular | perpendicular lines from right angles |
| Definition of a right angle | an angle that is exactly 90 degrees |
| Angle Addition Postulate | the addition of two angles to form the full angle |
| Vertical Angles Theorem | if two angles are vertical, then they are congruent |
| Complement Theorem | if two angles form a right angle, then they are complementary |
| Supplement Theorem | if two angles form a linear pair, then they are supplementary |
| Congruent Complements Theorem | if angle A is complementary to angle B and angle C is complementary to angle B, then angle A and angle C are congruent |
| Congruent Supplements Theorem | if angle A is supplementary to angle B and angle C is supplementary to angle B, then angle A is congruent to angle C |
Created by:
lesley_j
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