Question

1. use the diagram below to answer the following questions.

a) name all segments parallel to (overline{xt}).
b) name all segments parallel to (overline{zy}).
c) name all segments parallel to (overline{vs}).
d) name a plane parallel to plane (stu).
e) name a plane parallel to plane (uvz).
f) name all segments skew to (overline{sw}).
g) name all segments skew to (overline{ut}).

Explanation:

Step1: Recall parallel - segment concept

In a rectangular prism, parallel segments are segments that lie in parallel lines and never intersect.

Step2: Analyze segments parallel to $\overline{XT}$

Segments parallel to $\overline{XT}$ are $\overline{YS}$, $\overline{ZV}$, $\overline{WU}$.

Step3: Analyze segments parallel to $\overline{ZY}$

Segments parallel to $\overline{ZY}$ are $\overline{XT}$, $\overline{WU}$, $\overline{VS}$.

Step4: Analyze segments parallel to $\overline{VS}$

Segments parallel to $\overline{VS}$ are $\overline{ZY}$, $\overline{XT}$, $\overline{WU}$.

Step5: Recall parallel - plane concept

Parallel planes are planes that never intersect.

Step6: Find plane parallel to plane $STU$

The plane parallel to plane $STU$ is plane $VWZ$.

Step7: Find plane parallel to plane $UVZ$

The plane parallel to plane $UVZ$ is plane $XYT$.

Step8: Recall skew - segment concept

Skew segments are non - parallel and non - intersecting segments that do not lie in the same plane.

Step9: Find segments skew to $\overline{SW}$

Segments skew to $\overline{SW}$ are $\overline{XT}$, $\overline{ZY}$, $\overline{UV}$.

Step10: Find segments skew to $\overline{UT}$

Segments skew to $\overline{UT}$ are $\overline{ZV}$, $\overline{YW}$, $\overline{VS}$.

Answer:

a) $\overline{YS}$, $\overline{ZV}$, $\overline{WU}$
b) $\overline{XT}$, $\overline{WU}$, $\overline{VS}$
c) $\overline{ZY}$, $\overline{XT}$, $\overline{WU}$
d) Plane $VWZ$
e) Plane $XYT$
f) $\overline{XT}$, $\overline{ZY}$, $\overline{UV}$
g) $\overline{ZV}$, $\overline{YW}$, $\overline{VS}$