Properties of Equality

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 a*c = b*c

Division Property of Equality

If a = b, then a/c = b/c

Distributive Property

If a(b+c), then a(b+c) = ab+bc

Substitution Property

If a = b, then a may 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 ~= AB

Symmetric Property of Congruence

If AB ~= CD, then CD ~= AB

Transitive Property of Congruence

If AB ~= CD, and CD ~= EF, then AB ~= EF

Definition of Congruence

(segments are congruent if and only if they have the same measure.)

If AB ~= CD, then AB = CD

If AB = CD, then AB ~= CD

Definition of Midpoint

(the midpoint of a segment divides the segment into 2 equal (congruent) parts.)

If M is the midpoint of AB, then AM = BM

Segment Addition Postulate

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

Definition of Congruence

m <A = m<B ←→ <A ~= <B

Definition of Angle Bisector

An angle bisector divides an angle into two equal parts.

Definition of Complimentary Angles

complimentary ←→ sim is 90

Definition of Supplementary Angles

supplementary ←→ sim is 180

Definition of Perpendicular

perpendicular lines form right angles

Definition of a Right Angle

A right angle = 90

Angle Addition Postulate

m<ABD + <DBC = m<ABC

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. Right angle →complementary

Supplement Theorem

If two angles form a linear pair, then they are supplementary. Linear Pair → Supplementary

Congruent Complements Theorem

If <A is Complementary to <B and <C is complementary to <B, then <A ~= <C

Congruent Supplements Theorem

If <A is supplementary to <B and <C is supplementary to <B, then <A ~= <C