Question

(see example 2.) 6. name a pair of perpendicular lines. 8. is $overleftrightarrow{pr}perpoverleftrightarrow{np}$? explain. s of angles of the given type. (see example 3.) 10. alternate interior 12. consecutive interior

Explanation:

Step1: Identify perpendicular lines

Perpendicular lines form a 90 - degree angle. In the top - left figure, $\overleftrightarrow{NP}$ and $\overleftrightarrow{PR}$ are perpendicular as indicated by the right - angle symbol at their intersection. So a pair of perpendicular lines is $\overleftrightarrow{NP}$ and $\overleftrightarrow{PR}$.

Step2: Check if $\overleftrightarrow{PR}\perp\overleftrightarrow{NP}$

Since there is a right - angle symbol at the intersection of $\overleftrightarrow{PR}$ and $\overleftrightarrow{NP}$, by the definition of perpendicular lines (lines that intersect at a 90 - degree angle), $\overleftrightarrow{PR}\perp\overleftrightarrow{NP}$.

Step3: Find alternate interior angles

For two parallel lines cut by a transversal, alternate interior angles are non - adjacent angles between the two parallel lines and on opposite sides of the transversal. In the bottom figure, $\angle3$ and $\angle6$ are alternate interior angles, and also $\angle4$ and $\angle5$ are alternate interior angles.

Step4: Find consecutive interior angles

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

Answer:

1. $\overleftrightarrow{NP}$ and $\overleftrightarrow{PR}$
2. Yes, because there is a right - angle symbol at their intersection.
3. $\angle3$ and $\angle6$, $\angle4$ and $\angle5$
4. $\angle3$ and $\angle5$, $\angle4$ and $\angle6$