Use the diagram below to answer the following questions.

Name all segments parallel to XT.
Name all segments parallel to ZY.
Name all segments parallel to ZS.
Name a plane parallel to plane STU.
Name a plane parallel to plane UVZ.
Name all segments skew to SW.
Name all segments skew to UT.

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The following answers can be given as the solution to the given questions:

a) All segments parallel to XT:  YU, ZV, WS

b) All segments parallel to ZY:  VU, WX

c) All segments parallel to ZS:  YT

d) A plane parallel to plane STU: WXY

e) A plane parallel to plane UVZ:  TSW

f) All segments skew to SW:  ZY, VU, XY, UT

g) All segments skew to UT:  SW, WX, VZ, ZY

To give the appropriate answers to the given questions, the following terms must be understood.

i. Parallel lines: Two or more lines are parallel if and only if they do not meet even when extended to infinity.

ii. Skew lines: Two or more skew lines are lines that are neither parallel nor intersecting.

iii. Plane: This is flat surface which can either be in x-axis, y-axis or z-axis.

Therefore, the answers to each of the questions are:

a) All segments parallel to XT:  YU, ZV, WS

b) All segments parallel to ZY:  VU, WX

c) All segments parallel to ZS:  YT

d) A plane parallel to plane STU: WXY

e) A plane parallel to plane UVZ:  TSW

f) All segments skew to SW:  ZY, VU, XY, UT

g) All segments skew to UT:  SW, WX, VZ, ZY

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Segments parallel to XT: YU, ZV, WS

Segments parallel to ZY: VU, WX

Segments parallel to ZS: None

Plane parallel to plane STU: WXY

Plane parallel to plane UVZ: TSW

All segments skew to SW: WX, ST

All segments skew to UT: UY, TX

Step-by-step explanation:

Let's begin by explaining the following:

Two line segments are parallel only if their slopes are identical, allowing them to never intersect.

Hence, according to this definition we have:

Segments parallel to XT: YU, ZV, WS

Segments parallel to ZY: VU, WX

Segments parallel to ZS: None

Now, if we go to the three-dimensional space, two planes are parallel, when they do not share any line, which allows them to never cross in space.

Hence, according to this definition we have:

Plane parallel to plane STU: WXY

Plane parallel to plane UVZ: TSW

Two lines are skew if and only if they are not in the same plane (also known as not coplanar). So, if two lines are not coplanar, they are not parallel and cannot intersect, either.

Hence, according to this definition we have:

All segments skew to SW: WX, ST

WZ and SV do not match the condition, since they are in the same plane where SW is,

All segments skew to UT: UY, TX

UV and  ST do not match the condition, since they are in the same plane where UT is.