Proofs Involving the Triangle Inequality Theorem — Practice Geometry Questions

In geometry, the triangle inequality theorem states that when you add the lengths of any two sides of a triangle, their sum will be greater that the length of the third side.

By using the triangle inequality theorem and the exterior angle theorem, you should have no trouble completing the inequality proof in the following practice question.

Practice questions

Complete the following proof by adding the missing statement or reason.

Given:

Prove: ET > TV

1. What is the statement for Reason 2?

2. What is the reason for Statement 3?

3. What is the missing angle in Statement 4?

4. What is the reason for Statement 5?

5. What is the reason for Statement 6?

Answers and explanations

1. 

   A bisector divides an angle into two congruent angles.

2. The exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles.

   

   are the two nonadjacent interior angles of

   

   The exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles of the triangle; therefore,

   

3. 

   You found that

   

   The whole is greater than its parts, which means that

   

4. Transitive property

   Because

   

   the transitive property finds that

   

5. In a triangle, the longest side is opposite the largest angle.

   

   You discovered that

   

   In a triangle, the longest side is opposite the largest angle, so ET > TV.