5.5 Triangle Inequality Theorem

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 measure 8 and 15, what is the range of possible lengths for the third side?

Back

The range of possible lengths for the third side is between 7 and 23.

Front

What is the shortest side in a triangle with sides QP, QM, and MP if QM is the shortest?

Back

QM is the shortest side.

Front

Given two sides of lengths 6 and 15, what are the possible lengths for the third side?

Back

The possible lengths for the third side are between 9 and 21.

Front

Can the side lengths 4 cm, 7 cm, and 10 cm form a triangle?

Back

Yes, these lengths can form a triangle.

Front

Which of the following lengths cannot represent the sides of a triangle: 32, 34, 60, 28, 30, 58, 13, 20, 27, 2, 4, 5?

Back

The lengths that cannot represent the sides of a triangle are 28, 30, and 58.

Front

What is the minimum length of the third side if two sides of a triangle measure 10 and 14?

Back

The minimum length of the third side must be greater than 4.

Front

What is the maximum length of the third side if two sides of a triangle measure 10 and 14?

Back

The maximum length of the third side must be less than 24.

Front

If one side of a triangle is 5 and another is 12, what is the range for the third side?

Back

The range for the third side is between 7 and 17.

Front

What does it mean if the sum of two sides of a triangle is equal to the length of the third side?

Back

If the sum of two sides equals the length of the third side, the three points are collinear and do not form a triangle.