Geometry/Chapter 4/Lesson 2
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.
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.
Here, we have angles 85, 55 and x. We simply:
- Add 85 and 55 = 140
- 180 - 140
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.