1. Two Column Proofs Angles
∠A ≅ ∠B
Vertical angles are congruent A B
∠A ≅ ∠B
Alternate angles are congruent
∠A ≅ ∠D
Corresponding angles are congruent
∠A + ∠C = 180
Interior corresponding angles are supplementary C D A B

2. Alternate angles are congruent
∠4 ≅ ∠10
Corresponding angles are congruent
∠10 ≅ ∠14
∠4 ≅ ∠14
Transitive property of quality
∠14 + ∠15 = 180
Angles on a straight line are supplementary
∠4 + ∠15 = 180
Substitution property
∠4 and ∠15 are supplementary
Def of supplementary angles

3. Angles on a straight line are s
Right angle is 90
Subtraction property of equality
Vertical angles are congruent
Right angle is 90
Substitution property of equality
Transitive property of equality