Key Concepts: Proving Angle Relationships

Properties of Angle Congruence

• Reflexive: ∠A ≅ ∠A
• Symmetric: If ∠A ≅ ∠B, then ∠B ≅ ∠A
• Transitive: If ∠A ≅ ∠B and ∠B ≅ ∠C, then ∠A ≅ ∠C

Key Theorems

• Supplement Theorem: If two angles form a Linear Pair, they are supplementary.
• Complement Theorem: If the non-common sides of two adjacent angles form a right Angle, the angles are complementary.
• Vertical Angles Theorem: Vertical Angles are congruent.
• Congruent Supplements Theorem: If two angles are supplementary to the same Angle (or congruent angles), they are congruent.
• Congruent Complements Theorem: If two angles are complementary to the same Angle (or congruent angles), they are congruent.
• Right Angle Theorems: All right angles are congruent. Perpendicular lines form congruent adjacent angles.