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 a triangle has sides of lengths a, b, and c, what must be true?

Back

a + b > c, a + c > b, and b + c > a.

Front

Which of the following sets of lengths can form a triangle? 2, 3, 5; 4, 4, 8; 5, 5, 5; 1, 2, 3

Back

5, 5, 5 can form a triangle.

Front

Can the lengths 3, 4, and 9 form a triangle?

Back

No, because 3 + 4 is not greater than 9.

Front

What is the minimum length of the third side if two sides of a triangle are 5 and 7?

Back

The third side must be greater than 2 (5 - 7) and less than 12 (5 + 7).

Front

If the longest side of a triangle is 10, what must be true about the other two sides?

Back

The sum of the other two sides must be greater than 10.

Front

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

Back

Lengths 2, 2, and 5 cannot form a triangle.

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.

Front

If a triangle has sides of lengths 6, 8, and x, what is the range of possible values for x?

Back

x must be greater than 2 and less than 14.

Front

What is the significance of the longest side in a triangle?

Back

The longest side must be less than the sum of the other two sides.