Question

extra practice
in exercises 1 - 4, think of each segment in the diagram as part of a line.
which line(s) or plane(s) contain point b and appear to fit the description?

1. line(s) skew to (overline{fg})
2. line(s) perpendicular to (overline{fg})
3. line(s) parallel to (overline{fg})
4. plane(s) parallel to plane fgh

in exercises 5 - 8, use the diagram.

1. name a pair of parallel lines.
2. name a pair of perpendicular lines.
3. is (overline{wx}paralleloverline{qr})? explain.
4. is (overline{st}perpoverline{nv})? explain.

in exercises 9 - 12, identify all pairs of angles of the given type.

1. corresponding
2. alternate interior
3. alternate exterior
4. consecutive interior

Explanation:

Step1: Analyze line - plane relationships in 3 - D figure

For Exercises 1 - 4, in a 3 - D figure, we use the concepts of skew, perpendicular, and parallel lines and planes.

Step2: Identify parallel and perpendicular lines in 2 - D figure

For Exercises 5 - 8, we use the definitions of parallel and perpendicular lines in a 2 - D figure.

Step3: Recall angle - pair definitions

For Exercises 9 - 12, we recall the definitions of corresponding, alternate interior, alternate exterior, and consecutive interior angles formed by a transversal intersecting two or more lines.

1. There is no line containing point B that is skew to $\overline{FG}$ (assuming standard 3 - D rectangular - prism - like figure where point B is not in a position to have a skew line to $\overline{FG}$ passing through it).
2. Lines $\overline{AB}$ and $\overline{CB}$ (assuming a rectangular - prism - like figure) are perpendicular to $\overline{FG}$.
3. Lines $\overline{EH}$ and $\overline{DC}$ are parallel to $\overline{FG}$.
4. Plane $ABCD$ is parallel to plane $FGH$.
5. A pair of parallel lines in the second figure could be $\overline{SU}$ and $\overline{TV}$.
6. A pair of perpendicular lines in the second figure could be $\overline{SU}$ and $\overline{QR}$ (assuming right - angle symbol indicates perpendicularity).
7. $\overline{WX}$ is not parallel to $\overline{QR}$ as they intersect at point N.
8. $\overline{ST}$ is perpendicular to $\overline{NV}$ if the right - angle symbol at their intersection indicates perpendicularity.
9. Corresponding angles: $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$, $\angle9$ and $\angle13$ (not shown in given numbering but if more lines were there), $\angle10$ and $\angle14$, $\angle11$ and $\angle15$, $\angle12$ and $\angle16$.
10. Alternate interior angles: $\angle3$ and $\angle6$, $\angle4$ and $\angle5$, $\angle9$ and $\angle10$.
11. Alternate exterior angles: $\angle1$ and $\angle8$, $\angle2$ and $\angle7$, $\angle11$ and $\angle12$.
12. Consecutive interior angles: $\angle3$ and $\angle5$, $\angle4$ and $\angle6$, $\angle9$ and $\angle12$, $\angle10$ and $\angle11$.

Answer:

1. No such line.
2. $\overline{AB}$, $\overline{CB}$
3. $\overline{EH}$, $\overline{DC}$
4. Plane $ABCD$
5. $\overline{SU}$, $\overline{TV}$
6. $\overline{SU}$, $\overline{QR}$
7. No, they intersect at point N.
8. Yes if right - angle symbol indicates perpendicularity.
9. $\angle1$ and $\angle5$, $\angle2$ and $\angle6$, $\angle3$ and $\angle7$, $\angle4$ and $\angle8$, etc.
10. $\angle3$ and $\angle6$, $\angle4$ and $\angle5$, $\angle9$ and $\angle10$
11. $\angle1$ and $\angle8$, $\angle2$ and $\angle7$, $\angle11$ and $\angle12$
12. $\angle3$ and $\angle5$, $\angle4$ and $\angle6$, $\angle9$ and $\angle12$, $\angle10$ and $\angle11$