Chapter 11.1A, Problem 7A

The following figure is a rectangular box in which $EFGH$ and $ABCD$ are rectangles with $\overline{BF}$ and $\overline{DH}$ perpendicular to planes $FGH$ and $BCD$. Answer the following.

a. Name two pairs of skew lines.

b. Are $\stackrel{\leftrightarrow }{BD}$ and $\stackrel{\leftrightarrow }{FH}$ parallel, skew, or intersecting lines?

c. Are $\stackrel{\leftrightarrow }{BD}$ and $\stackrel{\leftrightarrow }{GH}$ parallel?

d. Find the intersection of $\stackrel{\leftrightarrow }{BD}$ and plane $EFG$ if possible.

e. Explain why planes $BDH$ and $FHG$ are perpendicular.