Lessons 2.4-2.5 Proofs

AC + CB = AB

• Addition Property of Equality

• Angle Addition Postulate

• Definition of Midpoint

• Segment Addition Postulate

If AC + CB = AB and AB = AC + AC, then AC + CB = AC + AC.

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive Property of Equality

If AC + CB = AC + AC, then CB = AC.

• Combine Like-Terms

• Simplify

• Subtraction Property of Equality

• Transitive Property of Equality

If CB = AC, then AC = CB.

• Reflexive Property of Equality

• Symmetric Property of Equality

• Transitive Property of Equality

• Definition of Congruent Angles

• Definition of Congruent Segments

• Reflexive Property of Congruence

• Symmetric Property of Congruence

• Definition of Congruent Angles

• Definition of Congruent Segments

• Symmetric Property of Congruence

• Vertical Angles Congruence Theorem

• Angle Addition Postulate

• Definition of Complementary Angles

• Definition of Supplementary Angles

• Linear Pair Postulate

• Angle Addition Postulate

• Right Angles Congruence Theorem

• Substitution Property of Equality

• Vertical Angles Congruence Theorem

• Addition Property of Equality

• Angle Addition Postulate

• Combine Like-Terms

• Multiplication Property of Equality

• Distributive Property

• Division Property of Equality

• Multiplication Property of Equality

• Subtraction Property of Equality