Geometry Postulates

Addition Property of Equality

if a=b and c=d, then a+c=b+d

Subtraction Property of Equality

if a=b and c=d, then a-c = b-d

Multiplication Property of Equality

If a = b, then ca = cb

Division Property of Equality

If a = b and c ≠ 0, then a/c = b/c

Substitution

If a=b, then either a or b may be substituted for the other in any equation

Reflexive

a = a

Symmetric

if a = b, the b = a

Transitive

If a = b and b = c, then a = c

Distributive Property

a(b+c) = ab+ac

Midpoint Theorem

if M is the midpoint of AB, then AM = ½ AB and MB = ½ AB

Definition of Midpoint

The two halves of the midpoint are equal to each other.

Angle Addition Postulate

Segment Addition Postulate

AB + BC = AC

Angle Bisector Theorem

Definition of Angle Bisector

divides an angle into two smaller, equal (congruent) angles

Def of Complementary Angles

Two angles that add up to 90 degrees

Def of Supplementary Angles

Two angles that add up to 180 degrees

Def of Perpendicular Lines

Two lines that Intersect to form Right Angles

If two lines are perpendicular, then they form congruent adjacent angles

If two lines for congruent adjacent angles, then the lines are perpendicular

If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary

If two angles are supplements of congruent angles, then the angles are congruent

If two angles are complements of congruent angles, then the two angles are congruent