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 are 27 and 39, what is the range for the length of the third side?

Back

The length of the third side must be between 12 and 66.

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

28, 30, and 58 cannot represent the sides of a triangle.

Front

Can the side lengths 3 ft, 5 ft, and 8 ft form a triangle?

Back

No, they cannot form a triangle.

Front

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

Back

Yes, they can form a triangle.

Front

If two sides of a triangle are 8 and 5, what is the range for the length of the third side?

Back

The length of the third side must be between 3 and 13.

Front

What is the minimum length of the third side if the other two sides are 5 and 8?

Back

The minimum length of the third side is 3.

Front

What is the maximum length of the third side if the other two sides are 5 and 8?

Back

The maximum length of the third side is 13.

Front

If the sides of a triangle are represented as a, b, and c, what must be true according to the Triangle Inequality Theorem?

Back

a + b > c, a + c > b, and b + c > a must all be true.

Front

What is an example of side lengths that cannot form a triangle?

Back

Side lengths 2, 4, and 5 cannot form a triangle because 2 + 4 is not greater than 5.