Question

given: n || m and ∠1 ≅ ∠2. prove: p || r. n is parallel to m, ∠1 is congruent to ∠2. ∠1 is congruent to ∠3. ∠2 is congruent to ∠3. p is parallel to r

Explanation:

Step1: Use given angle - congruence

Given $\angle1\cong\angle2$ and $\angle1\cong\angle3$. By the transitive property of congruence, $\angle2\cong\angle3$.

Step2: Apply parallel - line theorem

If two lines are cut by a transversal and corresponding angles are congruent, the lines are parallel. Since $\angle2$ and $\angle3$ are corresponding angles and $\angle2\cong\angle3$, we can conclude that $p\parallel r$.

Answer:

$p$ is parallel to $r$ because $\angle2\cong\angle3$ (by transitive property from $\angle1\cong\angle2$ and $\angle1\cong\angle3$) and they are corresponding angles formed by lines $p$, $r$ and a transversal.