Question

1. communicate and justify write a two - column proof of the alternate exterior angles theorem. given: m || n prove: ∠1≅∠2

Explanation:

Step1: State vertical - angle property

$\angle1\cong\angle3$ (Vertical angles are congruent)

Step2: State corresponding - angle property

Since $m\parallel n$, $\angle3\cong\angle2$ (Corresponding angles of parallel lines are congruent)

Step3: Use the transitive property

If $\angle1\cong\angle3$ and $\angle3\cong\angle2$, then $\angle1\cong\angle2$ (Transitive property of congruence)

Answer:

The two - column proof:

Statements	Reasons
2. $\angle1\cong\angle3$	Vertical angles are congruent
3. $\angle3\cong\angle2$	Corresponding angles of parallel lines are congruent
4. $\angle1\cong\angle2$	Transitive property of congruence