Triangle Inequality Practice

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If two sides of a triangle are 8 and 15, what is the range of possible lengths for the third side?

Back

The range is 7 < x < 23.

Front

Which of the following sets of lengths can form a triangle? {3, 4, 5}, {1, 2, 3}, {5, 10, 15}, {7, 8, 9}

Back

{3, 4, 5} and {7, 8, 9} can form a triangle.

Front

What is the minimum length of the third side if the other two sides are 10 and 14?

Back

The minimum length is 4 (10 - 14 < x).

Front

Can a triangle exist with sides of lengths 5, 5, and 10?

Back

No, it cannot exist because 5 + 5 is not greater than 10.

Front

What is the maximum length of the third side if the other two sides are 6 and 8?

Back

The maximum length is 13 (6 + 8 > x).

Front

If a triangle has sides of lengths 7, 10, and x, what is the range for x?

Back

The range is 3 < x < 17.

Front

What does it mean for a set of lengths to be 'not form a triangle'?

Back

It means that the lengths do not satisfy the Triangle Inequality Theorem.

Front

Given sides of lengths 9, 12, and 20, can these lengths form a triangle?

Back

No, because 9 + 12 is not greater than 20.

Front

What is the relationship between the sides of a triangle?

Back

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