Question

parallel lines
parallel planes
skew lines
examples!
1
a. name all segments parallel to ae.
b. give two examples of parallel planes.
(1) __________ (2) __________
c. name all segments skew to gh.
2
a. name all segments parallel to jr.
b. name all segments parallel to ng.
c. name a plane parallel to plane jkl.
d. name four segments skew to rq.

Explanation:

Step1: Recall parallel - line concept

Parallel lines are lines that do not intersect and are in the same plane. In a rectangular prism, for a segment like $\overline{AE}$, segments parallel to it are $\overline{BF}$, $\overline{CG}$, $\overline{DH}$ as they have the same direction and are in parallel planes.

Step2: Recall parallel - plane concept

Parallel planes are planes that do not intersect. In a rectangular prism, examples of parallel planes are the front - back planes (e.g., plane $ABCD$ and plane $EFGH$) and the top - bottom planes (e.g., plane $ABFE$ and plane $DCGH$).

Step3: Recall skew - line concept

Skew lines are lines that do not intersect and are not in the same plane. For a segment like $\overline{GH}$, segments skew to it are $\overline{AB}$, $\overline{CD}$, $\overline{EF}$, $\overline{AE}$, $\overline{BF}$, $\overline{DH}$ etc.

For the second figure:

Step4: Find parallel segments to $\overline{JK}$

Segments parallel to $\overline{JK}$ are those that have the same direction and are in parallel planes. They are segments that are parallel to it in the prism structure.

Step5: Find parallel segments to $\overline{NO}$

Similar to the above, find segments with the same direction and in parallel planes.

Step6: Find a parallel plane to plane $JKL$

A plane parallel to plane $JKL$ is a plane that does not intersect it and has the same orientation in the prism.

Step7: Find skew segments to $\overline{RQ}$

Segments that do not intersect $\overline{RQ}$ and are not in the same plane as it.

Answer:

1.
a. $\overline{BF}$, $\overline{CG}$, $\overline{DH}$
b. (1) Plane $ABCD$ and plane $EFGH$; (2) Plane $ABFE$ and plane $DCGH$
c. $\overline{AB}$, $\overline{CD}$, $\overline{EF}$, $\overline{AE}$, $\overline{BF}$, $\overline{DH}$
2.
a. (Answers depend on the prism structure, for example, if it is a standard prism - like figure, segments with the same direction in parallel planes)
b. (Answers depend on the prism structure)
c. (Answers depend on the prism structure, a plane with the same orientation and non - intersecting)
d. (Answers depend on the prism structure, segments that do not intersect $\overline{RQ}$ and are not in the same plane)