Question

given ∠1 ≅ ∠2
prove p || q
statements
1 ∠1 ≅ ∠2
reasons
1 given
correctly assemble the next statement

Explanation:

Step1: Vertical angles are congruent

$\angle1\cong\angle3$ (Vertical angles theorem)

Step2: Transitive property of congruence

Since $\angle1\cong\angle2$ (given) and $\angle1\cong\angle3$, then $\angle2\cong\angle3$ (Transitive property: if $a = b$ and $a = c$, then $b = c$)

Step3: Alternate - interior angles converse

If two lines are cut by a transversal and the alternate - interior angles are congruent, then the lines are parallel. Here, $\angle2$ and $\angle3$ are alternate - interior angles. So, $p\parallel q$ (Alternate - interior angles converse)

Answer:

1. $\angle1\cong\angle3$
2. $\angle2\cong\angle3$
3. $p\parallel q$