Question

statements reasons ∠1≅∠2 corresponding angles are congruent. ∠1≅∠3 alternate interior angles are congruent. ∠2≅∠3 transitive property of congruence statements reasons ∠1≅∠2 corresponding angles are congruent. ∠1≅∠3 corresponding angles are congruent. ∠2≅∠3 transitive property of congruence statements reasons ∠1≅∠2 alternate interior angles are congruent. ∠1≅∠3 corresponding angles are congruent. ∠2≅∠3 transitive property of congruence statements reasons ∠1≅∠2 corresponding angles are congruent. ∠1≅∠3 corresponding angles are congruent.

Explanation:

Step1: Identify $\angle1$ and $\angle2$

$\angle1$ and $\angle2$ are corresponding angles formed by parallel - lines $l$ and $m$ and transversal $n$. So, $\angle1\cong\angle2$ because corresponding angles are congruent.

Step2: Identify $\angle1$ and $\angle3$

$\angle1$ and $\angle3$ are corresponding angles formed by parallel - lines $n$ and $p$ and transversal $l$. So, $\angle1\cong\angle3$ because corresponding angles are congruent.

Step3: Use the transitive property

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

Answer:

The second set of statements and reasons (where $\angle1\cong\angle2$ because corresponding angles are congruent, $\angle1\cong\angle3$ because corresponding angles are congruent, and $\angle2\cong\angle3$ by the transitive property of congruence) is correct.