Geometry Proof Terms

Deductive Reasoning

Using general rules or facts to reach a specific logical conclusion.

Conditional Statement

A statement in “if–then” form (If p, then q).

Biconditional Statement

A statement combining two conditionals: “if and only if” (p ↔ q).

Colinear

Points that lie on the same straight line.

Noncolinear

Points that do not lie on the same line.

Integer

A whole number; can be positive, negative, or zero.

Definition of Congruency

Two figures are congruent if they have the same size and shape (equal measures).

Segment Addition Postulate (SAP)

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

Angle Addition Postulate (AAP)

If point B lies in the interior of ∠AOC, then m∠AOB + m∠BOC = m∠AOC.

Vertical Angle Theorem (VAT)

Vertical (opposite) angles are congruent.

Definition of Linear Pair

Two adjacent angles whose non

Linear Pair Postulate

If two angles form a linear pair, they are supplementary (sum to 180°).

Definition of Midpoint

A point that divides a segment into two congruent segments.

Midpoint Theorem

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

Definition of Bisector

A line, ray, or segment that divides another figure into two congruent parts.

Definition of Perpendicular Lines

Two lines that intersect to form right angles.

Definition of Right Angles

An angle that measures 90°.

Definition of Supplementary Angles

Two angles whose measures add up to 180°.

Definition of Complementary Angles

Two angles whose measures add up to 90°.

Congruent Supplements Theorem

If two angles are supplementary to the same angle (or congruent angles), then they are congruent.

Congruent Complements Theorem

If two angles are complementary to the same angle (or congruent angles), then they are congruent.

Reflexive Property

A quantity is equal (or congruent) to itself.

Symmetric Property

If one quantity equals another, the reverse is also true.

Transitive Property

If one quantity equals a second, and the second equals a third, then the first equals the third.

Addition Property

You can add the same value to both sides of an equation.

Subtraction Property

You can subtract the same value from both sides of an equation.

Multiplication Property

You can multiply both sides of an equation by the same nonzero number.

Division Property

You can divide both sides of an equation by the same nonzero number.

Substitution Property

If two values are equal, one can be replaced for the other in an expression.

Distributive Property

a(b + c) = ab + a