Question

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

a) name all segments parallel to (overline{xy}).
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}).
this is a 2 - page document!
homework 1: parallel lines & planes

Explanation:

Step1: Recall parallel and skew - line definitions

Parallel segments lie in the same plane and do not intersect, skew segments are non - coplanar and do not intersect. Planes are parallel if they do not intersect.

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

Segments parallel to $\overline{XY}$ are in the same orientation and in parallel planes. In the given prism, $\overline{SU}$, $\overline{TV}$, $\overline{ZW}$ are parallel to $\overline{XY}$.

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

Segments parallel to $\overline{ZY}$ are $\overline{TX}$, $\overline{SV}$, $\overline{UW}$.

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

Segments parallel to $\overline{VS}$ are $\overline{UW}$, $\overline{TX}$, $\overline{ZY}$.

Step5: Analyze planes parallel to plane $STU$

Planes parallel to plane $STU$ are plane $VWZ$.

Step6: Analyze planes parallel to plane $UVZ$

Planes parallel to plane $UVZ$ are plane $STW$.

Step7: Analyze segments skew to $\overline{SW}$

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

Step8: Analyze segments skew to $\overline{UT}$

Segments skew to $\overline{UT}$ are $\overline{ZW}$, $\overline{SV}$, $\overline{XY}$.

Answer:

a) $\overline{SU}$, $\overline{TV}$, $\overline{ZW}$
b) $\overline{TX}$, $\overline{SV}$, $\overline{UW}$
c) $\overline{UW}$, $\overline{TX}$, $\overline{ZY}$
d) Plane $VWZ$
e) Plane $STW$
f) $\overline{TX}$, $\overline{ZY}$, $\overline{UV}$
g) $\overline{ZW}$, $\overline{SV}$, $\overline{XY}$