**Introduction to Types of Triangles **

**Lesson Summary**

In this lesson, you will learn how to classify triangles according to the lengths of their sides and their angle measurements.

**I**t would be difficult to name an occupation where classifying triangles is a required skill; however, it is a skill that will help you solve complex geometry problems. Each of the triangles discussed in this lesson has special properties that will help you solve problems.

**Classification Triangles by Sides**

You can classify triangles by the lengths of their sides. On the next page are three examples of special triangles called *equilateral, isosceles*, and *scalene*.

To show that two or more sides of a triangle have the same measurement, a hatch mark is made through the congruent sides. Sometimes, two hatch marks are made on each congruent side, and sometimes, three hatch marks are made on each congruent side. You can match up the number of hatch marks to find which sides are congruent. You'll see these hatch marks in most geometry books. The symbol for congruent is .

**Isosceles Triangles**

Isosceles triangles are important geometric figures to understand. Some geometry books define isosceles as having at *least* two congruent sides. For our purposes, we will define isosceles as having exactly two congruent sides. Did you know that the parts of an isosceles triangle have special names? The two congruent sides of an isosceles triangle are called the *legs*. The angle formed by the two congruent sides is called the *vertex angle*. The other two angles are called the *base angles*. And finally, the side opposite the vertex angle is called the *base*.

**Example:**

**Classification Triangles by Angles**

You can also classify triangles by the measurements of their angles. Here are four examples of special triangles. They are called *acute, equiangular, right*, and *obtuse*.

To show that two or more angles of a triangle have the same measurement, a small curve is made in the congruent angles. You can also use two small curves to show that angles are congruent.

Practice problems for these concepts can be found at: Types of Triangles Practice Questions.

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