Question

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 prove p || r given n || m and <1 ≅ <2 reflexive property corresponding angles are congruent converse of corresponding angles given symmetric property alternate interior angles are congruent transitive/substitution property converse of alternate exterior angles alternate exterior angles are congruent converse of alternate interior angles

Explanation:

Step1: Use the given information

Given that $n\parallel m$ and $\angle1\cong\angle2$, $\angle1\cong\angle3$.

Step2: Apply transitive property

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

Step3: Use converse of alternate - interior angles

The converse of alternate - interior angles states that if alternate - interior angles are congruent, then the lines are parallel. $\angle2$ and $\angle3$ are alternate - interior angles for lines $p$ and $r$. Since $\angle2\cong\angle3$, 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 by the converse of alternate - interior angles.