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 $overline{ut}$.

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 $abc$ and plane $abf$
e) plane $aed$ and plane $bfc$
classify $angle1$ and $angle2$ on the diagram as corresponding, alternate interior, alternate exterior, consecutive (same - side) interior, or consecutive (same - side) exterior angles.
3.
4.
5.
6.
7.
8.

Explanation:

Step1: Recall parallel - segment and plane rules

In a three - dimensional figure, parallel segments lie in the same or parallel planes and do not intersect, and parallel planes do not intersect.

Step2: Analyze part 1a

In the first 3 - D figure, segments parallel to $\overline{XT}$ are $\overline{YZ}$, $\overline{VW}$.

Step3: Analyze part 1b

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

Step4: Analyze part 1c

Segments parallel to $\overline{VS}$ are $\overline{WT}$, $\overline{YU}$.

Step5: Analyze part 1d

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

Step6: Analyze part 1e

A plane parallel to plane $UVZ$ is plane $XWT$.

Step7: Analyze part 1f

Segments skew to $\overline{SW}$ are $\overline{XT}$, $\overline{YZ}$, $\overline{UV}$, $\overline{WT}$, $\overline{YU}$.

Step8: Analyze part 1g

Segments skew to $\overline{UT}$ are $\overline{VW}$, $\overline{YZ}$, $\overline{SW}$, $\overline{VS}$, $\overline{YU}$.

Step9: Analyze part 2a

$\overline{AB}$ and $\overline{BC}$ intersect at point $B$.

Step10: Analyze part 2b

$\overline{AE}$ and $\overline{BF}$ are skew.

Step11: Analyze part 2c

$\overline{EF}$ and $\overline{AD}$ are skew.

Step12: Analyze part 2d

Plane $ABC$ and plane $ABF$ intersect along line $\overline{AB}$.

Step13: Analyze part 2e

Plane $AED$ and plane $BFC$ are parallel.

Step14: Analyze part 3

$\angle1$ and $\angle2$ are alternate exterior angles.

Step15: Analyze part 4

$\angle1$ and $\angle2$ are corresponding angles.

Step16: Analyze part 5

$\angle1$ and $\angle2$ are consecutive (same - side) interior angles.

Step17: Analyze part 6

$\angle1$ and $\angle2$ are alternate interior angles.

Step18: Analyze part 7

$\angle1$ and $\angle2$ are consecutive (same - side) exterior angles.

Step19: Analyze part 8

$\angle1$ and $\angle2$ are corresponding angles.

Answer:

1a. $\overline{YZ}$, $\overline{VW}$
1b. $\overline{XT}$, $\overline{VW}$
1c. $\overline{WT}$, $\overline{YU}$
1d. plane $VWZ$
1e. plane $XWT$
1f. $\overline{XT}$, $\overline{YZ}$, $\overline{UV}$, $\overline{WT}$, $\overline{YU}$
1g. $\overline{VW}$, $\overline{YZ}$, $\overline{SW}$, $\overline{VS}$, $\overline{YU}$
2a. intersecting
2b. skew
2c. skew
2d. intersecting
2e. parallel

1. alternate exterior
2. corresponding
3. consecutive (same - side) interior
4. alternate interior
5. consecutive (same - side) exterior
6. corresponding