Proofs (better)

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 ac = bc.

Division Property of Equality

If a = b and c ≠ 0, then a/c = b/c.

Distributive Property of Equality

a(b + c) = ab + ac.

Substitution Property of Equality

If a = b, then b can replace a in any expression.

Simplify

Combine like terms or perform arithmetic to make an expression easier to work with.

Segment Addition Postulate

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

Angle Addition Postulate

If point D is in the interior of ∠ABC, then ∠ABD + ∠DBC = ∠ABC.

Linear Pair Postulate

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

Reflexive Property of Congruent Segments

A segment is congruent to itself: AB ≅ AB.

Symmetric Property of Congruent Segments

If AB ≅ CD, then CD ≅ AB.

Transitive Property of Congruent Segments

If AB ≅ CD and CD ≅ EF, then AB ≅ EF.

Reflexive Property of Congruent Angles

An angle is congruent to itself: ∠A ≅ ∠A.

Symmetric Property of Congruent Angles

If ∠A ≅ ∠B, then ∠B ≅ ∠A.

Transitive Property of Congruent Angles

If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C.

Right Angles Congruence Theorem

All right angles are congruent.

Congruent Supplements Theorem

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

Congruent Complements Theorem

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

Vertical Angles Congruence Theorem

Vertical angles are congruent.

Definition of Supplementary Angles

Two angles whose measures add to 180°.

Definition of Complementary Angles

Two angles whose measures add to 90°.

Definition of Vertical Angles

Angles opposite each other when two lines intersect.

Definition of Right Angles

An angle that measures exactly 90°.

Definition of a Midpoint

A point that divides a segment into two congruent parts.

Definition of Perpendicular Lines

Two lines that intersect to form right angles (90°).

Definition of Congruent Segments

Segments that have the same length.

Definition of Congruent Angles

Angles that have the same measure.

Corresponding Angles Congruence Theorem

If two parallel lines are cut by a transversal, corresponding angles are congruent.

Alternate Interior Angles Congruence Theorem

If two parallel lines are cut by a transversal, alternate interior angles are congruent.

Alternate Exterior Angles Congruence Theorem

If two parallel lines are cut by a transversal, alternate exterior angles are congruent.

Consecutive Interior Angles Postulate

If two parallel lines are cut by a transversal, consecutive interior angles are supplementary.

Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

If two triangles are congruent, then all their matching sides and angles are congruent.