Geometry/Chapter 4/Lesson 2

Introduction

We will learn how to classify triangles by their side and we will learn about the Triangle Angle-Sum Theorem.

Classifying Triangles by their Sides

As mentioned before, triangles can also be classified by their sides. To indicate the sides that congruent in a triangle, hash marks are drawn.

• 
  A scalene triangle is a triangle that has no sides that are congruent
• 
  An isosceles triangle is a triangle that has at least 2 sides that are congruent
• 
  An equilateral triangle is a triangle where all sides are congruent.

The Triangle Angle-Sum Theorem

• Theorem 2-1 (Triangle Angle-Sum Theorem) - The sum of the measures of the angles of a triangle is 180.

When we are hit with a "find x" problem, it should be easy for you (if it is dealing with a triangle!). All you do is add the angles that have been given to you (which will bring you j), then minus j from 180, and you have your answer! Let us implicate this procedure on an actual triangle problem.

Find x in this triangle

Here, we have angles 85, 55 and x. We simply:

• Add 85 and 55 = 140
• 180 - 140
• 40

x = 40 - If we want to double check this, we can always add all the angles up:

• 85 + 55 + 40 = 180

Per Theorem 2-1, all the angles should add up to 180 degrees.

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