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 side lengths are 7 yd, 8 yd, and 9 yd, can they form a triangle?

Back

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

Front

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

Back

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

Front

Which of the following sets of side lengths can form a triangle: 3, 6, 12; 7, 7, 14; 9, 9, 9; 13, 6, 7?

Back

9, 9, 9 can form a triangle.

Front

For the side lengths 11, 28, and 16, can a triangle be formed?

Back

No, because 11 + 16 is not greater than 28.

Front

What is the condition for three lengths a, b, and c to form a triangle?

Back

The conditions are: a + b > c, a + c > b, and b + c > a.

Front

If a triangle has sides of lengths 5, 5, and 10, can it exist?

Back

No, because 5 + 5 is not greater than 10.

Front

What is an example of side lengths that can form a triangle?

Back

Example: 6, 8, 10 (6 + 8 > 10, 6 + 10 > 8, 8 + 10 > 6).

Front

If the side lengths are 4, 4, and 8, can they form a triangle?

Back

No, because 4 + 4 is not greater than 8.

Front

What is the minimum requirement for two sides of a triangle?

Back

The sum of the lengths of the two shorter sides must be greater than the length of the longest side.