### Video Transcript

Identify a pair of points between
which diagonal of the cuboid can be drawn. Option (A) ๐ด and ๐ถ, option (B) ๐ธ
and ๐ท, option (C) ๐น and ๐ถ, option (D) ๐บ and ๐ท, option (E) ๐ด and ๐บ.

Here, we have a cuboid, which is
often sometimes seen as a rectangular prism. When weโre asked to draw a diagonal
of this cuboid, what weโre looking for is a line which passes through the interior
of the cuboid, often called a space diagonal. Notice that itโs different to a
face diagonal, which is a diagonal in two dimensions. So letโs say that the line is drawn
between ๐ท and ๐ต. We have then created a diagonal of
the plane ๐ด๐ต๐ถ๐ท. However, as this plane is in two
dimensions, we have only created a face diagonal. Therefore, this line would not be a
diagonal of the cuboid. In the same way, we could create
the line between ๐ป and ๐ถ. However, once again, weโve found a
diagonal of the plane, this time ๐ถ๐ท๐ป๐บ. And therefore, the diagonal would
be a face diagonal but not a diagonal of the cuboid.

So what would a diagonal of the
cuboid actually look like? Letโs say we wanted to start at
vertex ๐ป and create a diagonal from there. Drawing a line to vertex ๐ถ would
give us a face diagonal. So instead, traveling in three
dimensions through the interior of the cuboid would take us to vertex ๐ต. We can therefore say that ๐ป๐ต is
the diagonal of the cuboid. A diagonal of the cuboid starting
at vertex ๐ท and traveling through the interior of the cuboid would take us to
vertex ๐น.

And so ๐ท๐น is also a diagonal of
the cuboid. In fact, there are a total of four
space diagonals in a cuboid. Although itโs a little trickier to
see on this diagram, the line joining ๐ถ and ๐ธ is a diagonal. And finally, ๐ด๐บ is our fourth
diagonal. Out of the answer options, (A)
through (E), that we were given, the only one which is a pair of points between
which a diagonal can be drawn is option (E), ๐ด and ๐บ. The other four options here would
all create face diagonals.

Itโs important to note that when
weโre working with the diagonals of three-dimensional shapes, for example, if weโre
using the Pythagorean theorem, then the face diagonals will be a different length to
the space diagonals. For example, the diagonal ๐ต๐ป will
be longer than the face diagonal ๐ต๐ธ.