Question

geometric definitions iv
consider the figure shown.
which line is skewed to line ab?
a ad
b ae
c cg
d dc
which plane is parallel to plane cbfg?
a plane hefg
b plane aefb
c plane adhe
d plane dcgh

Explanation:

First Question

Step1: Recall the definition of skew lines

Skew lines are non - parallel and non - intersecting lines in 3D space.

• Line \(AD\) intersects line \(AB\) at point \(A\), so it is not skew.
• Line \(AE\) intersects line \(AB\) at point \(A\), so it is not skew.
• Line \(DC\) is parallel to line \(AB\) (in a rectangular prism, \(AB\parallel DC\) as they are opposite sides of a rectangle - like face \(ABCD\)), so it is not skew.
• Line \(CG\):
• Line \(AB\) is in the plane \(ABCD\) and line \(CG\) is in the plane \(BCGF\).
• They do not intersect (since \(AB\) and \(CG\) are not in the same plane and their extensions will not meet) and are not parallel.

Second Question

Step1: Recall the definition of parallel planes

Parallel planes are planes that do not intersect.

• Plane \(CBFG\) and plane \(ADHE\):
• In a rectangular prism, plane \(CBFG\) and plane \(ADHE\) are opposite planes.
• Plane \(CBFG\) has sides \(CB\), \(BF\), \(FG\), \(GC\) and plane \(ADHE\) has sides \(AD\), \(DH\), \(HE\), \(EA\).
• They do not intersect and are parallel.
• Plane \(HEFG\) intersects plane \(CBFG\) along the line \(FG\).
• Plane \(AEFB\) intersects plane \(CBFG\) along the line \(BF\).
• Plane \(DCGH\) intersects plane \(CBFG\) along the line \(CG\).

Answer:

1. C. \(CG\)
2. C. plane \(ADHE\)