Triangle Sum Theorem



In this lesson, we will learn

  • the Triangle Sum Theorem (with worksheets)
  • how to prove the Triangle Sum Theorem
  • how to solve problems using the Triangle Sum Theorem
Related Topics:
More Geometry Lessons

Geometry Worksheets

The Triangle Sum Theorem states that

The sum of the three interior angles in a triangle is always 180°.

The Triangle Sum Theorem is also called the Triangle Angle Sum Theorem or Angle Sum Theorem.

Example :





Example:

Find the value of x in the following triangle.

 

Solution:

x + 24° + 32° = 180° (sum of angles is 180°)

x + 56° = 180°

x = 180° – 56° = 124°

 

Worksheet 1, Worksheet 2 using Triangle Sum Theorem



Proof of the Triangle Sum Theorem

The follwing videos show how to prove that the sum of the angles of a triangle is 180 degrees. (Triangle Sum Theorem)





Solving problems using the Triangle Sum Theorem

The following videos show more examples of how to solve problems related to the triangle sum theorem using Algebra.

How to Find the Missing Angle in a Triangle Using the Triangle Sum Theorem



Use the traingle sum theorem to find the base angle measures given the vertex angle in an isosceles triangle.





Find the values of x and y for a given triangle problem. This problem uses the Triangle Sum Theorem and the Corollary to the Triangle Sum Theorem.



Find the values of x and y for a given triangle problem. This problem involves linear pair angles as well as the Triangle Sum Theorem.









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