Geometry/Chapter 4/Lesson 2

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Introduction[edit]

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[edit]

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

The Triangle Angle-Sum Theorem[edit]

  • 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.