Geometry Unit 2: Parallel Lines

Addition Property of Equality

If the same value is added to both sides of an equation, the equation stays equal.

Subtraction Property of Equality

If the same value is subtracted from both sides of an equation, the equation stays equal.

Multiplication Property of Equality

If both sides of an equation are multiplied by the same value, the equation stays equal.

Division Property of Equality

If both sides of an equation are divided by the same nonzero value, the equation stays equal.

Distributive Property

Multiply a value outside parentheses by each term inside the parentheses. Example: a(b + c) = ab + ac.

Substitution Property of Equality

If two values are equal, one can replace the other in an equation.

Reflexive Property of Equality

A quantity is equal to itself. Example: 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.

Reflexive Property of Congruence

A figure or angle is congruent to itself. Example: ∠A ≅ ∠A.

Symmetric Property of Congruence

If ∠A ≅ ∠B, then ∠B ≅ ∠A.

Transitive Property of Congruence

If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C.

Congruent Angles

Angles that have equal measures.

Definition of Congruence

If two angles have equal measures, then they are congruent. Example: m∠A = m∠B means ∠A ≅ ∠B.

Angle Bisector

A ray that divides an angle into two congruent angles.

Complementary Angles

Two angles whose measures add to 90°.

Supplementary Angles

Two angles whose measures add to 180°.

Perpendicular Lines

Two lines that intersect to form right angles.

Right Angle

An angle that measures exactly 90°.

Vertical Angles

Opposite angles formed when two lines intersect.

Vertical Angles Theorem

Vertical angles are congruent.

Complement Theorem

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

Supplement Theorem

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

Linear Pair

Two adjacent angles whose noncommon sides form a straight line; their measures add to 180°.

Congruent Complements Theorem

If two angles are complementary to the same angle, then the two angles are congruent.

Congruent Supplements Theorem

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

Angle Addition Postulate

Part + part = whole. If a point is inside an angle, the two smaller angle measures add to the measure of the entire angle.

Given

Information that is provided in the problem; usually the starting point of a proof.

To Prove

The statement or conclusion that the proof must show is true.

Statements

The facts and conclusions written in the left column of a two-column proof.

Reasons

The definitions, postulates, theorems, or properties that justify each statement in a proof.

Two-Column Proof

A proof organized with statements on the left and reasons on the right.

Definition

Explains the exact meaning of a mathematical term and can be used to justify a step in a proof.

Postulate

A mathematical statement accepted as true without proof.

Theorem

A mathematical statement that has been proven true and can be used to justify steps in a proof.

Property

A mathematical rule that can be used to justify operations or relationships in a proof.

Proof

A logical sequence of statements and reasons used to demonstrate that a mathematical conclusion is true.