Question

b. give two examples of parallel planes.
(1) __________________ & __________________
(2) __________________ & __________________
c. name all segments skew to \\(\overline{gh}\\). ____________________
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:

To solve these problems, we analyze the geometric figures (likely prisms or cubes) and use properties of parallel planes, parallel segments, and skew segments.

Part 1 (Top Figure, Likely a Cube/Prism)

b. Parallel Planes

In a rectangular prism (or cube), opposite faces are parallel.
(1) Example 1: Plane \( F \) (e.g., front face) and Plane \( B \) (e.g., back face) (adjust labels to match the figure; common pairs: top/bottom, front/back, left/right).
(2) Example 2: Plane \( Top \) and Plane \( Bottom \) (or other opposite faces).

c. Segments Skew to \( \overline{GH} \)

Skew segments do not intersect and are not parallel. For \( \overline{GH} \) (vertical/edge), skew segments are non - intersecting, non - parallel edges. E.g., \( \overline{AB}, \overline{CD}, \overline{EF} \) (adjust to figure’s labels; depends on \( GH \)’s orientation).

Part 2 (Bottom Figure, Likely a Prism)

a. Segments Parallel to \( \overline{JK} \)

In a prism, edges parallel to \( \overline{JK} \) are congruent and parallel. E.g., \( \overline{LM}, \overline{NP}, \overline{QR} \) (depends on prism structure).

b. Segments Parallel to \( \overline{NS} \)

Parallel segments to \( \overline{NS} \) are those with the same direction. E.g., \( \overline{MR}, \overline{PQ}, \overline{JK} \) (adjust to figure).

c. Plane Parallel to Plane \( JKL \)

In a prism, planes containing opposite bases are parallel. E.g., Plane \( MNP \) (if \( JKL \) and \( MNP \) are bases).

d. Segments Skew to \( \overline{RQ} \)

Skew segments to \( \overline{RQ} \) do not intersect and are not parallel. E.g., \( \overline{JK}, \overline{LM}, \overline{NS}, \overline{NP} \) (adjust to figure’s edges).

Final Answers (Sample, Depends on Exact Figure Labels)

Part 1b

(1) Plane \( ABCD \) & Plane \( EFGH \) (if a cube with these faces)
(2) Plane \( ABFE \) & Plane \( DCGH \)

Part 1c

\( \overline{AB}, \overline{CD}, \overline{EF} \)

Part 2a

\( \overline{LM}, \overline{NP}, \overline{QR} \)

Part 2b

\( \overline{MR}, \overline{PQ}, \overline{JK} \)

Part 2c

Plane \( MNP \)

Part 2d

\( \overline{JK}, \overline{LM}, \overline{NS}, \overline{NP} \)

(Note: Replace labels with the actual figure’s vertex/face labels for precision.)

Answer:

To solve these problems, we analyze the geometric figures (likely prisms or cubes) and use properties of parallel planes, parallel segments, and skew segments.

Part 1 (Top Figure, Likely a Cube/Prism)

b. Parallel Planes

In a rectangular prism (or cube), opposite faces are parallel.
(1) Example 1: Plane \( F \) (e.g., front face) and Plane \( B \) (e.g., back face) (adjust labels to match the figure; common pairs: top/bottom, front/back, left/right).
(2) Example 2: Plane \( Top \) and Plane \( Bottom \) (or other opposite faces).

c. Segments Skew to \( \overline{GH} \)

Skew segments do not intersect and are not parallel. For \( \overline{GH} \) (vertical/edge), skew segments are non - intersecting, non - parallel edges. E.g., \( \overline{AB}, \overline{CD}, \overline{EF} \) (adjust to figure’s labels; depends on \( GH \)’s orientation).

Part 2 (Bottom Figure, Likely a Prism)

a. Segments Parallel to \( \overline{JK} \)

In a prism, edges parallel to \( \overline{JK} \) are congruent and parallel. E.g., \( \overline{LM}, \overline{NP}, \overline{QR} \) (depends on prism structure).

b. Segments Parallel to \( \overline{NS} \)

Parallel segments to \( \overline{NS} \) are those with the same direction. E.g., \( \overline{MR}, \overline{PQ}, \overline{JK} \) (adjust to figure).

c. Plane Parallel to Plane \( JKL \)

In a prism, planes containing opposite bases are parallel. E.g., Plane \( MNP \) (if \( JKL \) and \( MNP \) are bases).

d. Segments Skew to \( \overline{RQ} \)

Skew segments to \( \overline{RQ} \) do not intersect and are not parallel. E.g., \( \overline{JK}, \overline{LM}, \overline{NS}, \overline{NP} \) (adjust to figure’s edges).

Final Answers (Sample, Depends on Exact Figure Labels)

Part 1b

(1) Plane \( ABCD \) & Plane \( EFGH \) (if a cube with these faces)
(2) Plane \( ABFE \) & Plane \( DCGH \)

Part 1c

\( \overline{AB}, \overline{CD}, \overline{EF} \)

Part 2a

\( \overline{LM}, \overline{NP}, \overline{QR} \)

Part 2b

\( \overline{MR}, \overline{PQ}, \overline{JK} \)

Part 2c

Plane \( MNP \)

Part 2d

\( \overline{JK}, \overline{LM}, \overline{NS}, \overline{NP} \)

(Note: Replace labels with the actual figure’s vertex/face labels for precision.)