Triangle Inequality Theorem Concepts

This video lesson covers 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 provides examples to illustrate this concept, showing both valid and invalid sets of side lengths for forming triangles. It includes practice problems to reinforce understanding and application of the theorem.

What does the triangle inequality theorem state?

• The sum of the lengths of all three sides of a triangle is equal to zero.

• The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

• The sum of the lengths of any two sides of a triangle is equal to the length of the third side.

• The sum of the lengths of any two sides of a triangle is less than the length of the third side.

In the example with side lengths 4, 5, and 7, why do these lengths form a triangle?

• Because 4 + 5 is greater than 7, 5 + 7 is greater than 4, and 4 + 7 is greater than 5.

• Because 5 + 7 is less than 4.

• Because 4 + 5 is less than 7.

• Because 4 + 5 is equal to 7.

Why can't the side lengths 4, 2, and 7 form a triangle?

• Because 4 + 2 is equal to 7.

• Because 4 + 2 is less than 7.

• Because 4 + 2 is greater than 7.

• Because 7 + 2 is less than 4.

Given side lengths 3, 6, and 10, can these form a triangle?

• Yes, because 3 + 6 is greater than 10.

• No, because 3 + 6 is less than 10.

• Yes, because 3 + 10 is greater than 6.

• No, because 6 + 10 is less than 3.

If two sides of a triangle are 4 inches and 6 inches, what should be the third side to form a triangle?

• 5 inches

• 11 inches

• 10 inches

• 7 inches

Why is 10 inches not a suitable length for the third side when the other two sides are 4 inches and 6 inches?

• Because 4 + 6 is equal to 10.

• Because 4 + 6 is greater than 10.

• Because 10 is less than 4.

• Because 4 + 6 is less than 10.

What is the correct third side length for a triangle with sides 4 inches and 6 inches?

• 8 inches

• 9 inches

• 10 inches

• 7 inches

What is the importance of the triangle inequality theorem?

• It helps in determining the type of triangle.

• It helps in determining if three given lengths can form a triangle.

• It helps in calculating the area of a triangle.

• It helps in finding the perimeter of a triangle.

Which of the following sets of side lengths can form a triangle?

• 7, 10, 12

• 2, 3, 5

• 6, 8, 15

• 5, 5, 10

What is the result of adding the side lengths 7 and 10 in the example provided?

• 15

• 18

• 17

• 19