Geometry and Triangles - All Types

When we want to learn about geometry and triangles, we have to group them into certain categories.

Categorized by Angles

The sum of the angles of a triangle is 180°. 

A right triangle has one angle of 90° and looks like the ones below.  Why can't it have two or three angles of 90°? 

An acute triangle is a triangle where all three angles are acute.  An acute angle is between 0 and 90 degrees.  For more information about angles, look here.  The triangles below are all acute. 

A special type of acute triangle is a triangle where  all three angles are equal.  This is known as an equiangular triangle. Equiangular meaning "equal angles."
 

Finally, an triangle is called obtuse if it has one obtuse angle in it - an angle between 90 and 180 degrees.  Take a look at the obtuse triangles below.

Categorized by Side Length

Triangles can also be grouped according to their side lengths.  These names have nothing to do with the angles of the triangle.  In other words, you could describe a triangle using one of the terms above (acute, right, obtuse) and also with one of the words below.

If none of the side lengths are the same size, the triangle is said to be scalene.

If at least two of the sides are equal, then the triangle is said to be isosceles.  The "tick marks" (little dashes) indicate that the sides are equal in length. 

If all three of the sides are equal, then the triangle is called isosceles (notice the definition above says "at least two sides"), but it is also given the special name of equilateral.  Equilateral means "equal sides."

Making Connections - Geometry and Triangles

The interesting thing about these definitions is that they often overlap.  We can have a triangle that is both right and isosceles; or scalene and acute.  Take a look back at the terms and see how many possibilities you can come up with.

When solving problems in geometry that involve triangles, be sure to set up your equations correctly.  Set things equal when they are equal, and add them up when necessary.  For example, don't forget that adding all the angles of a triangle will always be equal to 180°.  Are you now confident you know all about geometry and triangles?

More geometry and triangle properties will be updated shortly, so be sure to check back.  Also, be certain that you check out our geometry worksheets section for easy opportunities to practice.  Otherwise return to the free geometry help page for more available topics.