Question

given: ∠1 and ∠3 are supplementary prove: m||n statements reasons 1. ∠1 and ∠3 are supplementary 1. 2. m∠1 + m∠3 = 180° 2. 3. 3. vertical angle congruence thm. 4. m∠2 = m∠3 4. 5. 5. substitution property of equality 6. 6. definition of supplementary angles 7. m||n 7.

Explanation:

Step1: Given information

Given

Step2: Definition of supplementary angles

Definition of supplementary angles

Step3: $\angle2\cong\angle3$

$\angle2$ and $\angle3$ are vertical - angles

Step4: Congruent angles have equal measures

Definition of congruent angles

Step5: Substitute $m\angle2$ for $m\angle3$ in $m\angle1 + m\angle3=180^{\circ}$

$m\angle1 + m\angle2 = 180^{\circ}$

Step6: $\angle1$ and $\angle2$ are supplementary

Since $m\angle1 + m\angle2 = 180^{\circ}$

Step7: Converse of same - side interior angles postulate

If same - side interior angles are supplementary, then the lines are parallel

Answer:

1. Given
2. Definition of supplementary angles
3. $\angle2\cong\angle3$
4. Definition of congruent angles
5. $m\angle1 + m\angle2 = 180^{\circ}$
6. $\angle1$ and $\angle2$ are supplementary
7. Converse of same - side interior angles postulate