# Video: Identifying the Pair of Points between Which a Diagonal of the Cuboid Can Be Drawn

Identify a pair of points between which diagonal of the cuboid can be drawn. [A] 𝐴, 𝐶. [B] 𝐸, 𝐷. [C] 𝐹, 𝐶. [D] 𝐺, 𝐷. [E] 𝐴, 𝐺.

02:33

### Video Transcript

Identify a pair of points between which diagonal of the cuboid can be drawn. Option (A) 𝐴 and 𝐶, option (B) 𝐸 and 𝐷, option (C) 𝐹 and 𝐶, option (D) 𝐺 and 𝐷, option (E) 𝐴 and 𝐺.

Here, we have a cuboid, which is often sometimes seen as a rectangular prism. When we’re asked to draw a diagonal of this cuboid, what we’re looking for is a line which passes through the interior of the cuboid, often called a space diagonal. Notice that it’s different to a face diagonal, which is a diagonal in two dimensions. So let’s say that the line is drawn between 𝐷 and 𝐵. We have then created a diagonal of the plane 𝐴𝐵𝐶𝐷. 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 𝐻 and 𝐶. However, once again, we’ve found a diagonal of the plane, this time 𝐶𝐷𝐻𝐺. 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? Let’s say we wanted to start at vertex 𝐻 and create a diagonal from there. Drawing a line to vertex 𝐶 would give us a face diagonal. So instead, traveling in three dimensions through the interior of the cuboid would take us to vertex 𝐵. We can therefore say that 𝐻𝐵 is the diagonal of the cuboid. A diagonal of the cuboid starting at vertex 𝐷 and traveling through the interior of the cuboid would take us to vertex 𝐹.

And so 𝐷𝐹 is also a diagonal of the cuboid. In fact, there are a total of four space diagonals in a cuboid. Although it’s a little trickier to see on this diagram, the line joining 𝐶 and 𝐸 is a diagonal. And finally, 𝐴𝐺 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), 𝐴 and 𝐺. The other four options here would all create face diagonals.

It’s important to note that when we’re working with the diagonals of three-dimensional shapes, for example, if we’re using the Pythagorean theorem, then the face diagonals will be a different length to the space diagonals. For example, the diagonal 𝐵𝐻 will be longer than the face diagonal 𝐵𝐸.