Question

1. $\angle 1$ is supplementary to $\angle 2$.2. $m\angle 1 + m\angle 2 = 180^\circ$3. $p \parallel q$4. $\angle 2 \cong \angle 3$5. $m\angle 2 = m\angle 3$6. $m\angle 1 + m\angle 3 = 180^\circ$7. $\angle 1$ is supplementary to $\angle 3$.8. $r \parallel s$reasonsbankconsecutive interior angles conversealternate interior angles theoremdefinition of supplementary angles ($\times2$)substitution property of equalitygiven ($\times2$)definition of congruent angles

Explanation:

Step1: Match Statement 1 to reason

Statement 1 is given, so use "Given".

Step2: Match Statement 2 to reason

Statement 2 comes from definition of supplementary angles (sum = $180^\circ$), so use "Definition of supplementary angles".

Step3: Match Statement 3 to reason

Statement 3 is given, so use "Given".

Step4: Match Statement 4 to reason

Statement 4 is congruent angles, so use "Definition of congruent angles".

Step5: Match Statement 5 to reason

Statement 5 uses congruent angle measures, so use "Definition of congruent angles".

Step6: Match Statement 6 to reason

Statement 6 substitutes $\angle2$ with $\angle3$, so use "Substitution Property of Equality".

Step7: Match Statement 7 to reason

Statement 7 is from supplementary angle definition, so use "Definition of supplementary angles".

Step8: Match Statement 8 to reason

Statement 8 uses converse of consecutive interior angles, so use "Consecutive Interior Angles Converse".

Answer:

1. Given
2. Definition of supplementary angles
3. Given
4. Definition of congruent angles
5. Definition of congruent angles
6. Substitution Property of Equality
7. Definition of supplementary angles
8. Consecutive Interior Angles Converse