Chapter 3, Problem 7MCQ

To determine

Find all segments parallel to $\overline{HE}$ in the given figure.

Answer to Problem 7MCQ

  $\overline{FG}$ , $\overline{BC}\text{ and }\overline{DA}$

Explanation of Solution

Given :

  

Calculation :

Parallel segments are those that do not intersect and have equal distance between them at each point when a perpendicular is drawn.

So, we can find segments in the plane EFGH containing the segment $\overline{HE}$ and in the plane parallel to EFGH , that are parallel to $\overline{HE}$ .

Parallel planes are those that do not intersect . Since the opposite sides of the cube/cuboid never intersect, so , ABCD is the plane parallel to the plane EFGH in the figure as they are opposite faces of the given cube/cuboid.

The segment $\overline{FG}$ is parallel to $\overline{HE}$ since it is the opposite edge of the bottom square/rectangle.

Now, the line segments $\overline{BC}\text{ and }\overline{DA}$ lie in the plane parallel to the plane containing the line segment $\overline{HE}$ and are aligned in the same direction as $\overline{HE}$ .So, they are also parallel to $\overline{HE}$ .

So, $\overline{FG}$ , $\overline{BC}\text{ and }\overline{DA}$ are parallel to $\overline{HE}$ .