Standard types of triangles

Equilateral, isosceles, scalene

One way to categorize triangles goes like this:

• If all three angles of a triangle are the same size, then all three sides are the same length, and vice-versa. Such a triangle is called equilateral (which literally means “equal sides”).
• If there’s a two-way tie for angle size, then there’s also a two-way tie for side length (and vice-versa). This triangle is called isosceles (pronounced eye-SAUCE-uh-leez).
• If all three angles are different, then all three sides are different too. This kind of triangle is called scalene (pronounced SKAY-leen).

Every triangle belongs in one and only one of the above categories. Take a moment and see whether you can come up with a convincing argument why this should be true.

Acute, right, obtuse

Another way to categorize triangles relates to how big the angles are. It goes like this:

• If all three angles are smaller than 90 degrees, then the triangle is called acute (because all the angles are acute. As you might know, acute is the word we use to describe an angle that measures less than 90 degrees).
• If one of the angles is a right angle (i.e. if it measures exactly 90 degrees), then the triangle (and that angle) are both called right.
  • Note: in this case, the long side is called the hypotenuse, and the other two sides are called legs.
• If one of the angles is larger than a right angle, then the triangle (and that angle) are both called obtuse.

Notice that I didn’t mention triangles with more than one right angle, or more than one obtuse angle, or with both a right angle and an obtuse angle. Why didn’t I talk about any of those triangles?