Question

ideo for extra example 3 – proving theorems about parallel lines
rite a two - column proof.
given ∠1 is supplementary to ∠2 and p ∥ q
prove r ∥ s
two - column proof
statements reasons

1. ∠1 is supplementary to ∠2. 1.
2. m∠1 + m∠2 = 180° 2.
3. p ∥ q 3.
4. ∠2 ≅ ∠3 4.
5. m∠2 = m∠3 5.
6. m∠1 + m∠3 = 180° 6.
7. ∠1 is supplementary to ∠3. 7.
8. r ∥ s 8.

reasons bank
consecutive interior angles converse
alternate interior angles theorem
definition of supplementary angles (× 2)
substitution property of equality
given (× 2)
definition of congruent angles

Explanation:

Step1: Match given statement

Reason for Statement 1: Given

Step2: Use supplementary angle definition

Reason for Statement 2: Definition of supplementary angles

Step3: Match given parallel lines

Reason for Statement 3: Given

Step4: Apply alternate interior angles theorem

Reason for Statement 4: Alternate Interior Angles Theorem

Step5: Use congruent angles definition

Reason for Statement 5: Definition of congruent angles

Step6: Substitute equal angle measures

Reason for Statement 6: Substitution Property of Equality

Step7: Use supplementary angle definition

Reason for Statement 7: Definition of supplementary angles

Step8: Apply consecutive angles converse

Reason for Statement 8: Consecutive Interior Angles Converse

Answer:

STATEMENTS	REASONS
2. $m\angle 1 + m\angle 2 = 180^\circ$	2. Definition of supplementary angles
3. $p \parallel q$	3. Given
4. $\angle 2 \cong \angle 3$	4. Alternate Interior Angles Theorem
5. $m\angle 2 = m\angle 3$	5. Definition of congruent angles
6. $m\angle 1 + m\angle 3 = 180^\circ$	6. Substitution Property of Equality
7. $\angle 1$ is supplementary to $\angle 3$.	7. Definition of supplementary angles
8. $r \parallel s$	8. Consecutive Interior Angles Converse