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 the sides of a triangle are 3, 5, and 8, will they form a triangle?

Back

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

Front

What are the conditions for three lengths to form a triangle?

Back

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

Front

Can the lengths 7, 7, and 14 form a triangle?

Back

No, because 7 + 7 is not greater than 14.

Front

Which of the following sets of lengths can form a triangle: 3, 6, 12 or 9, 9, 9?

Back

9, 9, 9 can form a triangle.

Front

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

Back

Lengths 28, 30, and 58 cannot form a triangle.

Front

If a triangle has sides of lengths 5, 12, and 13, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 5 + 12 > 13, 5 + 13 > 12, and 12 + 13 > 5.

Front

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

Back

The minimum length of the third side must be greater than 2 (10 - 8).

Front

What is the maximum length of the third side if two sides of a triangle are 8 and 10?

Back

The maximum length of the third side must be less than 18 (8 + 10).

Front

If the sides of a triangle are 4, 5, and x, what is the range of possible values for x?

Back

x must be greater than 1 and less than 9.