Angle Proofs

Definition of Congruence

m∠A = m∠B ↔ ∠A ≅ ∠B

Definition of Angle Bisector

divides an angle into two equal parts

Definition of Complementary Angles

Sum is 90°

Definition of Supplementary Angles

Sum is 180°

Definition of Right Angle

A right angle = 90°

Angle Addition Postulate

m∠ABD + m∠DBC = m∠ABC

Vertical Angles Theorem

If two angles are vertical, then they are congruent.

Complement Theorem

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

Right Angle → Complementary

Supplement Theorem

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

Linear pair → Supplementary

Congruent Complements Theorem

If ∠A is complementary to ∠B and ∠C is complementary to ∠B, then ∠A ≅ ∠C

Congruent Supplements Theorem

If ∠A is supplementary to ∠B and ∠C is supplementary to ∠B, then ∠A ≅ ∠C