Chapter 11.5, Problem 45SR

To determine

To Find: The segments that are skew to $\overline{DC}$ .

Answer to Problem 45SR

The segments are $\overline{AL},\overline{BM},\overline{EP},\overline{NM},\overline{OP},\overline{PL},\overline{ML}$

Explanation of Solution

Given:

The given diagram is shown in Figure 1

  

Figure 1

Calculation:

To determine the lines that are skew to $\overline{DC}$ one should first find the plane that contains $\overline{DC}$ and find the line intersecting the plane at points not on $\overline{CD}$

From the figure, plane ABCDE contains $\overline{DC}$ so the segment $\overline{AL},\overline{BM},\overline{EP}$ are skew to $\overline{DC}$ .

Plane CDON contains $\overline{DC}$ , so the segments $\overline{NM}$ , $\overline{OP}$ are skew to $\overline{DC}$ .

Also, the segment $\overline{PL}$ and $\overline{ML}$ are skew to $\overline{DC}$ as they are on the plane parallel to $\overline{DC}$ and not parallel to. $\overline{DC}$

Thus, the segments are $\overline{AL},\overline{BM},\overline{EP},\overline{NM},\overline{OP},\overline{PL},\overline{ML}$ .