Proof Reasons (Honors)

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Angle Addition Postulate

if point B lies in the interior of

Definition of Congruent Angles

angles that have the same measure are congruent

Definition of Congruent Segments

segments that have the same length are congruent

Definition of Midpoint

A point that divides a segment into two congruent segments

Definition of Bisector

a line or segment that intersects a segment or angle and divides it into two congruent halves

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 is not equal to 0, then a/c = b/c

Substitution Property of Equality

If a=b, then b can be substituted for a in any expression

Distributive Property

a(b + c) = ab + ac

Reflexive Property of Equality

a = a

Symmetric Property of Equality

if a=b, then b=a

Transitive Property of Equality

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

Definition of Supplementary Angles

Two angles whose sum is 180 degrees

Definition of Complementary Angles

Two angles whose sum is 90 degrees

Vertical Angles Theorem

Vertical angles are congruent

Congruent Supplements Theorem

If two angles are supplementary to the same angle, then they are congruent

Congruent Complements Theorem

if two angles are complementary to the same angle, then they are congruent

Right Angle Congruence Theorem

All right angles are congruent

Linear Pairs Theorem

If two angles form a linear pair, then they are supplementary

simplify

to write an expression in a simpler form