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Adv. Geometry

Postulates, Theorums, and Definitions

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