Parts of a Prism

Meet the right triangular prism:

As can be seen, the right triangular prism consists of two triangles and three straight lines. Hence its name - triangular and right prism.
The prism consists of:
$2$ bases, $3$ heights and $3$ rectangles which are also called faces.

The bases of the prism are the $2$ triangles that compose it.
In our illustration they are marked in green.

The bases - the triangles - will always be identical.
The triangles can be isosceles, equilateral, scalene, or any other type of triangles. The important thing is to know that they will always be identical to each other.
That is, triangle $ABC$ is identical to triangle $DEF$

In a right triangular prism there are $3$ heights. The heights connect between the upper base of the prism to the lower base.
That is, heights $AD$, $BE$, $CF$ -

The heights are identical and equal in length to each other.

The prism consists of three rectangles which are its faces.
That is:
First rectangle $ACFD$
Second rectangle $BCFE$
Third rectangle $ABED$

• Each face has a pair of opposite sides - the heights and another pair of opposite sides that are the base of the prism.
• The sides that make up the base of the prism are not necessarily equal - after all, the triangles can also be scalene, and therefore the sides that make up the faces of the prism are not necessarily equal to each other.

A case where all faces are equal:
If the triangles of the prism are equilateral, all rectangles will be identical - all composed of equal sides.

A case where only $2$ faces are identical:
If the triangular bases of the prism are isosceles triangles, only $2$ of the faces will be identical and the third face will be different.

A case where all faces are different:
If the triangles of the prism are composed of scalene triangles, all faces will be different from one another.

How can we know this pattern without memorizing it?
Think about it this way: the face is actually a rectangle composed of heights and a triangle's side.
The heights are identical for each rectangle, so we only need to check the triangle's sides.

If the triangle is equilateral, it means that each rectangle will be made up of the same side and therefore they will be identical rectangles.
If the triangle is isosceles, it means there are only $2$ equal sides and therefore there will be only $2$ identical rectangles.
If the triangle is scalene, it means all sides are different and therefore there will be 3 different rectangles.

Now that we have deeply understood all the properties of a triangular right prism, let's move on to practice!

Determine whether True or False and explain:
a. A triangular right prism has $3$ triangles.
b. The triangular bases in a prism must be identical.
c. The triangles that make up the prism must be equilateral.
d. All rectangles must be identical in a triangular right prism.
e. All heights are equal in a triangular right prism.

Solution:
a. False. There are $2$ triangles that make up the bases of the prism.
b. True. The triangular bases will always be identical to each other.
c. False. The triangles can be equilateral, isosceles, or scalene.
d. False. The rectangles will be identical only if the prism's triangles are equilateral.
e. True. In a right triangular prism, all heights are equal in length.