Question

1. complete the two - column proof. given: $ellparallel m$, $angle1congangle2$ prove: $aparallel b$ statements reasons 1. $ellparallel m$ 1. 2. $angle1congangle3$ 2. 3. $angle1congangle2$ 3. 4. $angle2congangle3$ 4. 5. $aparallel b$ 5.

Explanation:

Step1: Given information

1. Given

Step2: Corresponding - angles postulate

If two parallel lines are cut by a transversal, corresponding angles are congruent. Since $\ell\parallel m$, $\angle1\cong\angle3$.

Step3: Given information

Given

Step4: Transitive property of congruence

If $\angle1\cong\angle3$ and $\angle1\cong\angle2$, then $\angle2\cong\angle3$ by the transitive property of congruence.

Step5: Converse of corresponding - angles postulate

If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel. Since $\angle2\cong\angle3$, $a\parallel b$.

Answer:

1. Given
2. Corresponding - angles postulate
3. Given
4. Transitive property of congruence
5. Converse of corresponding - angles postulate