Exploring the Triangle Inequality Theorem

What does the Triangle Inequality Theorem state?

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

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

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

• The sum of the lengths of any two sides of a triangle must be less than or equal to the length of the third side.

Why can't a triangle have sides of lengths 1, 1, and 2?

• Because 1 + 1 is equal to 2, not greater.

• Because 1 + 1 is equal to 3.

• Because 1 + 1 is less than 2.

• Because 1 + 1 is greater than 2.

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

• 1, 2, 3

• 4, 5, 10

• 8, 9, 10

• 2, 3, 15

If a triangle has sides of lengths 4 and 9, what is the range of possible values for the third side?

• 5 < x < 13

• 4 < x < 9

• 1 < x < 10

• 6 < x < 12

What is the lower boundary for the third side of a triangle with sides 8 and 10?

• 2

• 18

• 10

• 8

For sides 1 and 2, what is the range of the third side?

• 1 < x < 3

• 2 < x < 4

• 3 < x < 5

• 1 < x < 2

What is the upper boundary for the third side of a triangle with sides 5 and 14?

• 5

• 14

• 19

• 9

If a triangle has sides 4 and 4, what is the range of the third side?

• 2 < x < 6

• 3 < x < 5

• 1 < x < 7

• 0 < x < 8

Which of the following is a valid triangle with sides 1, 2, and 2?

• 1 + 2 is less than 2

• 1 + 2 is greater than 2

• 1 + 2 is not greater than 2

• 1 + 2 is equal to 2

How many possible triangles can be created using the side lengths 1, 2, 3, and 4?

• 13

• 11

• 10

• 12