Question

main ideas/questions notes/examples parallel lines that never are used to indicate the lines are parallel symbolic notation: parallel planes that never symbolic notation: skew lines that never examples: & & & example 1 a. name all segments parallel to $overline{ae}$. b. give two examples of parallel planes (1) & (2) & c. name all segments skew to $overline{gh}$. example 2 a. name all segments parallel to $overline{jk}$. b. name all segments parallel to $overline{ns}$. c. name a plane parallel to plane $jkl$. d. name four segments skew to $overline{rq}$.

Explanation:

Step1: Define parallel lines

Parallel lines are lines that never intersect. The symbol for parallel is $\parallel$.

Step2: Define parallel planes

Parallel planes are planes that never intersect. The symbol for parallel planes is also $\parallel$.

Step3: Define skew lines

Skew lines are non - coplanar lines that never intersect.

Step4: Solve Example 1 - Part a

In a rectangular prism, for a segment $\overline{AE}$, segments parallel to it are $\overline{DH},\overline{BF},\overline{CG}$ because they are in the same direction and will never intersect.

Step5: Solve Example 1 - Part b

Two examples of parallel planes in a rectangular prism could be plane $ABCD$ & plane $EFGH$ and plane $ABFE$ & plane $DCGH$.

Step6: Solve Example 1 - Part c

Segments skew to $\overline{GH}$ in a rectangular prism are $\overline{AB},\overline{CD},\overline{AE},\overline{BF}$ etc. as they are non - coplanar and do not intersect $\overline{GH}$.

Step7: Solve Example 2 - Part a

For a segment $\overline{JK}$ in a given prism, find segments in the same direction that don't intersect it.

Step8: Solve Example 2 - Part b

For a segment $\overline{NS}$, find parallel segments.

Step9: Solve Example 2 - Part c

For a plane $JKL$, find a parallel plane.

Step10: Solve Example 2 - Part d

For a segment $\overline{RQ}$, find four non - coplanar non - intersecting segments.

Answer:

Example 1:
a. $\overline{DH},\overline{BF},\overline{CG}$
b. (1) plane $ABCD$, plane $EFGH$; (2) plane $ABFE$, plane $DCGH$
c. $\overline{AB},\overline{CD},\overline{AE},\overline{BF}$

(Note: Answers for Example 2 depend on the specific prism in the figure and would follow similar logic as Example 1 for finding parallel and skew elements)