Triangle Inequality Theorem Concepts

The 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. It provides examples to demonstrate how to determine if three sides can form a triangle. The tutorial concludes with additional tips on applying the theorem effectively.

What is the basic rule of the triangle inequality theorem?

• 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.

• 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 less than the third side.

In the example with sides 3, 9, and 11, why can these form a triangle?

• Because 3 + 9 is greater than 11.

• Because 3 + 9 is equal to 11.

• Because 3 + 9 is less than 11.

• Because 3 + 9 is equal to 9.

Which of the following sets of sides cannot form a triangle?

• 5, 7, 10

• 8, 15, 20

• 3, 4, 8

• 6, 8, 13

Why is it often sufficient to only add the two smaller numbers when testing the triangle inequality?

• Because it guarantees the largest side is considered.

• Because it simplifies the calculation.

• Because it will always determine if the sides can form a triangle.

• Because it ensures the smallest side is considered.

What should you do if the sum of the two smaller sides is equal to the third side?

• It forms an isosceles triangle.

• It forms a right triangle.

• It cannot form a triangle.

• It can form a triangle.