Video Transcript
Using the rectangular prism below,
decide which of the following is skew to the line 𝐶𝐺. Option (A) the line 𝐻𝐺, option
(B) the line 𝐷𝐶, option (C) the line 𝐸𝐻, option (D) the line 𝐹𝐵, or option (E)
the line 𝐶𝐵.
We can recall that skew lines are
lines that do not intersect and are not parallel. They are noncoplanar, which means
they don’t lie on the same plane, and therefore they can only exist in three
dimensions. So, let’s highlight the line 𝐶𝐺
on the diagram. Because we’re looking for a line
which is skew to the line 𝐶𝐺, then that line can’t be parallel to the line 𝐶𝐺,
nor can it intersect this line. There are in fact a few different
lines which can be said to be skew to the line 𝐶𝐺 in this diagram.
Firstly, we have the line 𝐴𝐷. The line 𝐸𝐻 is also skew to the
line 𝐶𝐺, so is the line 𝐴𝐵 and the line 𝐸𝐹. So, there are four different lines
on this diagram that we can identify as being skew to the line 𝐶𝐺. However, only one of them appears
in the given list of answer options. So, our answer is that given in
option (C). It’s the line 𝐸𝐻.
However, before we finish with this
question, we can double-check the answer options to see what relationship those
lines have with the line 𝐶𝐺. Answer option (A) gives the line
𝐻𝐺. However, this line will be
perpendicular to the line 𝐶𝐺 because they lie on the same plane and they intersect
at 90 degrees. In the same way, in option (B), the
line 𝐷𝐶 we know will also intersect at 90 degrees. 𝐷𝐶 and 𝐶𝐺 are two perpendicular
lines.
In option (D), the line 𝐹𝐵 can be
seen as parallel to the line 𝐶𝐺. And finally, the line 𝐶𝐵 given in
option (E) will also be perpendicular to the line 𝐶𝐺. As none of these other four options
are lines which are skew to the line 𝐶𝐺, then there is just one possible
answer. It’s the line 𝐸𝐻.
