Geometry for Beginners - How To Classify Triangles

Welcome to Geometry for Beginners. In this article, we will be continue discussing triangles.

We have already defined "triangle" and discussed the formulas for both perimeter and area. This article will involve classifying triangles and we will be increasing our vocabulary with several words that will likely be new to you--not just different meanings for common words, but completely new words.

As has been mentioned in other articles, vocabulary is one of the main stumbling blocks for success in Geometry, so it is important that you take the time now to thoroughly understand these new words. Triangles have many possible shapes, and we use characteristics of these shapes as guides when classifying triangles.
One of these characteristics is angle size within the triangle; so we need to first review the various types of angles before discussing triangles.
Types of angles: 1.

Acute -- An angle between 0 and 90 degrees. 2.

Right -- An angle of exactly 90 degrees.

3.
Obtuse -- An angle between 90 and 180 degrees.
Note: A triangle can never have an angle greater than or equal to 180 degrees because the sum of all 3 angles of a triangle must total exactly 180 degrees. This is a very important fact that you will need throughout both Geometry and Trigonometry. Learn it now.
Triangles consist of six parts--three sides and three angles--and they can be classified by either their sides or their angles.
Since we just reviewed the labels for angles, let's start with that classification process.

Triangle Classification by Angles: 1.

Acute Triangle -- A triangle in which all 3 angles are acute.
2.
Right Triangle -- A triangle with exactly one right angle. Since the total of the 3 angles is 180 degrees, if 1 angle measures 90 degrees, the remaining two angles must be acute.
3. Obtuse Triangle -- A triangle with exactly one obtuse angle. Again, the remaining two angles must be acute.

A special case of acute triangle, Equiangular Triangle, happens if all three angles are equal.
Since the total of all 3 angles is exactly 180 degrees, if all three angles are equal, they must each measure 60 degrees.

Thus, if we are told either that all 3 angles of a triangle are equal or that each angle of a triangle measures 60 degrees, the triangle is called equiangular. Triangle Classification by Sides: (Caution! New Words Ahead!) 1.
Scalene Triangle (pronounced: skay'-lean) -- A triangle with NO equal sides.
2. Isosceles Triangle (pronounced: eye-sauce'-el-eze) -- A triangle with at least two equal sides. 3.

Equilateral Triangle --A triangle with all three sides of equal length.

It is important to know that these systems of classification can overlap. For example, an equilateral triangle is also equiangular, so knowing one fact, tells you the other as well. In addition, if a triangle is isosceles, the angles opposite those equal sides are also equal.
Thus, knowing we have 2 equal angles also tells us the triangle is isosceles. In a right triangle, if both legs are equal, then we have a right-isosceles triangle.
I hope you are beginning to see the need to be extremely clear in your mind about the meanings of all these new terms. Any confusion will cause disaster.

Since the triangle is one of the most fundamental concepts in Geometry, in Trigonometry, and in life in general, mastering the terminology will make your future much more successful.

Learn it NOW!