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

Given side lengths 7 yd, 8 yd, and 9 yd, can a triangle be formed?

Back

Yes, because 7 + 8 > 9, 7 + 9 > 8, and 8 + 9 > 7.

Front

What is the range of values for the third side x if two sides are 4 and 12?

Back

The range is between 8 and 16.

Front

Will the side lengths 16 cm, 35 cm, and 18 cm form a triangle?

Back

No, because 16 + 18 is not greater than 35.

Front

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

Back

No, because 3 + 5 is not greater than 8.

Front

Which set of side lengths does NOT form a triangle? {2, 5, 9}, {3, 4, 5}, {5, 10, 12}, {7, 9, 11}

Back

{2, 5, 9} does not form a triangle.

Front

If one side of a triangle is 10, what must be the range of the other two sides if they are 6 and x?

Back

x must be greater than 4 and less than 16.

Front

What is the minimum length of the third side if two sides are 8 and 10?

Back

The minimum length is 3, because 8 + 3 > 10.

Front

What is the maximum length of the third side if two sides are 5 and 7?

Back

The maximum length is 11, because 5 + 7 > 11.

Front

If the sides of a triangle are 5, 12, and x, what is the range for x?

Back

x must be between 7 and 17.