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 (stuv)
e) name a plane parallel to plane (uvzy)
f) name all segments skew to (overline{sw})
g) name all segments skew to (overline{ut})

1. using the diagram below, describe the relationship as parallel, intersecting, or skew.

a) (overline{ab}) and (overline{bc})
b) (overline{ae}) and (overline{bf})
c) (overline{ef}) and (overline{ad})
d) plane (abcd) and plane (abfe)
e) plane (aed) and plane (bfc)
use the diagram below to answer the following questions.
f) name a transversal.
g) name all corresponding angles.
h) name all alternate interior angles.
i) name all alternate exterior angles.
j) name all consecutive interior angles.
use the diagram below to answer the following questions.
a) name the transversal connecting (angle1) and (angle5).
b) name the transversal connecting (angle7) and (angle14).
c) name the transversal connecting (angle8) and (angle11).
d) name the transversal connecting (angle6) and (angle15).
e) name the transversal connecting (angle3) and (angle9).

Explanation:

Step1: Recall parallel segment definition

Parallel segments in 3 - D are segments that lie in the same plane and do not intersect. For the first cube - shaped figure:
a) Segments parallel to $\overline{XT}$ are $\overline{ZY}$, $\overline{WU}$, $\overline{VS}$.
b) Segments parallel to $\overline{ZY}$ are $\overline{XT}$, $\overline{WU}$, $\overline{VS}$.
c) Segments parallel to $\overline{VS}$ are $\overline{XT}$, $\overline{ZY}$, $\overline{WU}$.
d) A plane parallel to plane $STUV$ is plane $WXYZ$.
e) A plane parallel to plane $UVZY$ is plane $WXTS$.
f) Skew segments to $\overline{SW}$ are $\overline{XT}$, $\overline{ZY}$, $\overline{WU}$, $\overline{TV}$.
g) Skew segments to $\overline{UT}$ are $\overline{WX}$, $\overline{ZY}$, $\overline{VS}$, $\overline{ZW}$.

Step2: Recall line - line and plane - plane relationship definitions

For the second figure:
a) $\overline{AB}$ and $\overline{BC}$ are intersecting (they share a common point $B$).
b) $\overline{AE}$ and $\overline{BF}$ are parallel (they are in the same plane and do not intersect).
c) $\overline{EF}$ and $\overline{AD}$ are skew (they are not in the same plane and do not intersect).
d) Plane $ABCD$ and plane $ABFE$ are intersecting (they share the line $\overline{AB}$).
e) Plane $AED$ and plane $BFC$ are parallel (they do not intersect).

Step3: Recall transversal and angle - pair definitions

For the third figure:
f) A transversal is a line that intersects two or more lines. Here, the line that intersects the two given lines is the vertical line.
g) Corresponding angles are $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$.
h) Alternate interior angles are $\angle3$ and $\angle6$, $\angle4$ and $\angle5$.
i) Alternate exterior angles are $\angle1$ and $\angle8$, $\angle2$ and $\angle7$.
j) Consecutive interior angles are $\angle3$ and $\angle5$, $\angle4$ and $\angle6$.

Step4: Identify transversals for angle - pairs

For the fourth figure:
a) The transversal connecting $\angle1$ and $\angle5$ is line $r$.
b) The transversal connecting $\angle7$ and $\angle14$ is line $s$.
c) The transversal connecting $\angle8$ and $\angle11$ is line $p$.
d) The transversal connecting $\angle6$ and $\angle15$ is line $q$.
e) The transversal connecting $\angle3$ and $\angle9$ is line $p$.

Answer:

a) $\overline{ZY}$, $\overline{WU}$, $\overline{VS}$
b) $\overline{XT}$, $\overline{WU}$, $\overline{VS}$
c) $\overline{XT}$, $\overline{ZY}$, $\overline{WU}$
d) plane $WXYZ$
e) plane $WXTS$
f) $\overline{XT}$, $\overline{ZY}$, $\overline{WU}$, $\overline{TV}$
g) $\overline{WX}$, $\overline{ZY}$, $\overline{VS}$, $\overline{ZW}$
a) intersecting
b) parallel
c) skew
d) intersecting
e) parallel
f) the vertical line
g) $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$
h) $\angle3$ and $\angle6$, $\angle4$ and $\angle5$
i) $\angle1$ and $\angle8$, $\angle2$ and $\angle7$
j) $\angle3$ and $\angle5$, $\angle4$ and $\angle6$
a) line $r$
b) line $s$
c) line $p$
d) line $q$
e) line $p$