Question

(see example 2.)

1. name a pair of perpendicular lines.
2. is $overline{pr}perpoverline{np}$? explain.

s of angles of the given type. (see example 3.)

1. alternate interior
2. consecutive interior

Explanation:

Step1: Recall perpendicular - lines definition

Perpendicular lines form a 90 - degree angle. In the given figure, we check the angle between $\overline{PR}$ and $\overline{NP}$.

Step2: Analyze the figure

We can see from the figure that $\overline{PR}$ and $\overline{NP}$ intersect at a right - angle (90 degrees). So, $\overline{PR}\perp\overline{NP}$.

Step3: Recall alternate - interior angles definition

Alternate interior angles are non - adjacent angles that lie between two lines and on opposite sides of a transversal. In the second figure, $\angle3$ and $\angle6$ are alternate interior angles, also $\angle4$ and $\angle5$ are alternate interior angles.

Step4: Recall consecutive - interior angles definition

Consecutive interior angles are non - adjacent angles that lie between two lines and on the same side of a transversal. In the second figure, $\angle3$ and $\angle5$ are consecutive interior angles, also $\angle4$ and $\angle6$ are consecutive interior angles.

Answer:

1. Yes, $\overline{PR}\perp\overline{NP}$ because they intersect at a 90 - degree angle.
2. $\angle3$ and $\angle6$, $\angle4$ and $\angle5$
3. $\angle3$ and $\angle5$, $\angle4$ and $\angle6$