Triangle Inequality Theorem Concepts

This video tutorial explains the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. The video uses diagrams and animations to illustrate why this condition is necessary for forming a triangle. It also provides examples to demonstrate how to apply the theorem by checking if the sum of the two shorter sides is greater than the longest side. The tutorial emphasizes understanding the theorem's practical application in determining the possibility of forming a triangle with given side lengths.

What does the triangle inequality theorem state about the sides of a triangle?

• The sum of the lengths of any two sides must be less than the third side.

• The sum of the lengths of any two sides must be equal to the third side.

• The sum of the lengths of any two sides must be greater than the third side.

• The sum of the lengths of all three sides must be equal.

In the investigation with diagrams, what happens when the sum of two sides is less than the third side?

• The segments do not touch, and no triangle is formed.

• The segments overlap.

• A triangle is formed.

• The segments form a straight line.

What is demonstrated by the animation regarding the triangle inequality theorem?

• A triangle can be formed regardless of the side lengths.

• A triangle can be formed only if the sum of two sides is greater than the third side.

• A triangle can be formed if the sum of two sides is equal to the third side.

• A triangle can be formed if the sum of two sides is less than the third side.

Why can't a triangle be formed if the sum of two sides equals the third side?

• The sides overlap.

• The sides form a straight line.

• The sides are too long.

• The sides are too short.

In the first example, why is a triangle possible with sides of lengths 3, 4, and 6?

• Because 3 + 4 is less than 6.

• Because 3 + 4 is much greater than 6.

• Because 3 + 4 is equal to 6.

• Because 3 + 4 is greater than 6.

In the second example, why is a triangle not possible with sides of lengths 5, 6, and 11?

• Because 5 + 6 is much greater than 11.

• Because 5 + 6 is greater than 11.

• Because 5 + 6 is equal to 11.

• Because 5 + 6 is less than 11.

In the last example, why is a triangle not possible with sides of lengths 2, 3, and 9?

• Because 2 + 3 is less than 9.

• Because 2 + 3 is equal to 9.

• Because 2 + 3 is greater than 9.

• Because 2 + 3 is much greater than 9.

What should be checked to determine if three lengths can form a triangle?

• The sum of all three sides.

• The sum of the two shortest sides.

• The sum of the two longest sides.

• The sum of the longest side and the shortest side.

What is the key condition for forming a triangle according to the triangle inequality theorem?

• The sum of all three sides must be equal.

• The sum of any two sides must be greater than the third side.

• The sum of any two sides must be equal to the third side.

• The sum of any two sides must be less than the third side.

Why is it unnecessary to check the sum of every two sides when applying the triangle inequality theorem?

• Because only the longest side matters.

• Because only the shortest side matters.

• Because checking the sum of the two shortest sides is sufficient.

• Because checking the sum of the two longest sides is sufficient.