Question

1. that contain the segments in the figure and the figure. all angles are right - angles. 2. line(s) perpendicular to $overrightarrow{cd}$ 4. plane(s) parallel to plane $cdh$ (see example 2.) 6. name a pair of perpendicular lines. 8. is $overrightarrow{pr}perpoverrightarrow{np}$? explain. of angles of the given type. (see example 3.) 10. alternate interior 12. consecutive interior

Explanation:

Step1: Analyze perpendicular lines to $\overrightarrow{CD}$ in the rectangular - box

In a rectangular - box, lines perpendicular to a given line lie in planes that are perpendicular to the plane containing the given line. For $\overrightarrow{CD}$, the lines $\overrightarrow{BC}$, $\overrightarrow{AD}$, $\overrightarrow{FG}$, $\overrightarrow{EH}$ are perpendicular to it.

Step2: Find planes parallel to plane $CDH$

In a rectangular - box, parallel planes are opposite to each other. The plane parallel to plane $CDH$ is plane $ABF$.

Step3: Name a pair of perpendicular lines

In the second figure, $\overrightarrow{NP}$ and $\overrightarrow{PR}$ are perpendicular as indicated by the right - angle symbol at their intersection.

Step4: Determine if $\overrightarrow{PR}\perp\overrightarrow{NP}$

Yes, $\overrightarrow{PR}\perp\overrightarrow{NP}$ because there is a right - angle symbol at the intersection of the two lines, which means the angle between them is $90^{\circ}$.

Step5: Identify alternate interior angles

In the third figure, alternate interior angles are non - adjacent angles between two parallel lines and on opposite sides of a transversal. The pairs of alternate interior angles are $\angle3$ and $\angle6$, $\angle4$ and $\angle5$.

Step6: Identify consecutive interior angles

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

Answer:

1. $\overrightarrow{BC}$, $\overrightarrow{AD}$, $\overrightarrow{FG}$, $\overrightarrow{EH}$
2. Plane $ABF$
3. $\overrightarrow{NP}$ and $\overrightarrow{PR}$
4. Yes, because there is a right - angle symbol at their intersection.
5. $\angle3$ and $\angle6$, $\angle4$ and $\angle5$
6. $\angle3$ and $\angle5$, $\angle4$ and $\angle6$