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Adv. Geometry
Postulates, Theorums, and Definitions
| Question | Answer |
|---|---|
| Segment Addition Postulate | If B is between A and C, the AB+BC=AC |
| Angle Addition Postulate | If ∠AOC is a straight angle and B is any point not on ray AC, the m∠AOB+m∠BOC=180 |
| Addition Property | If a=b and c=d, then a+c=b+d |
| Subtraction Property | If a=b and c=d, then a-c=b-d |
| Multiplication Property | If a=b, then ca=cb |
| Division Property | If a=b and c≠0, then a/c=b/c |
| Substitution Property | If a=b then either a or b may be substituted for the other in any equation (or inequality) |
| Reflexive Property | a=a |
| Symmetric Property | If a=b then b=a |
| Transitive Property | if a=b and b=c, then a=c |
| Midpoint Theorem | If M is the midpoint of AB, then AM=1/2AB and MB=1/2AB |
| The Angle Bisector Theorem | If BX is the bisector of ∠ABC, then m∠ABX=1/2m∠ABC and m∠XBC=1/2m∠ABC |
| Vertical Angles Theorem | Vertical angles are congruent |
| Perpendicular to Congruent Theorem | If two lines are perpendicular, then they form congruent adjacent angles. |
| Congruent to Perpendicular Theorem | If two lines form congruent adjacent angles, then they are perpendicular. |
| Exterior with Perpendicular to Complimentary Theorem | If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary |
| Supplementary Theorem | If two angles are supplements of congruent angles (or the same angle), then the two angles are congruent |
| Complimentary Theorem | If two angles are compliments of congruent angles (or of the same angle), then the two angles are congruent |
Created by:
patrij16
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