2-4 Angle Proofs Review

Definition of Congruence

If measures are equal, then parts are congruent. (m?A = m?B then ?A ? ?B)

Definition of Angle Bisector

An angle bisector divides an angle into two equal parts

Definition of Complementary Angles

Two angles are complementary if their sum is 90 degrees

Definition of Supplementary Angles

Two angles whose sum is 180 degrees

Definition of Perpendicular

Perpendicular lines form right angles

Definition of a Right Angle

A right angle = 90 degrees

Angle Addition Postulate

If P is in the interior of <RST, then m<RSP + m<PST = m<RST

Vertical Angles Theorem

If two angles are vertical angles, then they are congruent.

Complements Theorem

If two angles form a right angle, then they are complementary

Supplements Theorem

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

Reflexive Property

A quantity is congruent (equal) to itself. ?A = ?A

Symmetric Property

If a = b, then b = a

Transitive Property

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

Linear Pair

A pair of adjacent angles whose noncommon sides are opposite rays. (2 angles that make a straight angle)

Adjacent Angles

Angles that have a common side and a common vertex (corner point).

Substitution Property of Equality

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

Distributive Property

a(b + c) = ab + ac

Addition Property of Equality

If you add the same number to each side of an equation, the two sides remain equal.

Subtraction Property of Equality

If you subtract the same number from each side of an equation, the two sides remain equal.

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