Comprehensive Review of Key Definitions, Postulates, Properties, and Theorems for Initial Proofs (Chapters 1-2)

Reflexive Property of Congruence

Symmetric Property of Congruence

Transitive Property of Congruence

Linear Pair

Angle Addition Postulate

Segment Addition Postulate

Reflexive Property of Equality

Symmetric Property of Equality

If a = b, then b = a

Transitive Property of Equality

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

Distributive Property

Addition/Subtraction Property of Equality

The same number can be added to/subtracted from both sides of an equation.

Multiplication/Division Property of Equality

multiplying (or dividing) by the same number on each side of an equation produces an equivalent equation

Definition of Congruent Angles

Two angles are congruent if and only if they are equal in measure.

Definition of Congruent Segments

Two segments are congruent if and only if they have the same length.

Definition of Midpoint

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

Definition of Angle Bisector

Definition of a Right Angle

An angle is a right angle if and only if it measures 90 degrees

Definition of a Straight Angle

An angle is a straight angle if and only if it measures 180 degrees.

Definition of Supplementary Angles

two angles whose degree measures have a sum of 180º

Definition of Complementary Angles

two angles whose degree measures have a sum of 90º

Vertical Angle Theorem

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

Definition of Perpendicular

two lines, segments, or rays are perpendicular if and only if the angles formed by their intersection are right angles (angles that measure 90 degrees

Converse of "If p then q"

If q then p

Inverse of "If p then q"

If not p then not q

Contrapositive of "If p then q"

If not q then not p

biconditional statement

a statement that can be written in the form "p if and only if q" as long as the conditional and converse are both true.