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 5, 7, and 12, does it satisfy the Triangle Inequality Theorem?

Back

No, because 5 + 7 = 12, which is not greater than 12.

Front

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

Back

The lengths a, b, and c must satisfy: a + b > c, a + c > b, and b + c > a.

Front

Can the lengths 3, 4, and 8 form a triangle?

Back

No, because 3 + 4 = 7, which is not greater than 8.

Front

What is the shortest side in a triangle with sides 6, 8, and 10?

Back

6 is the shortest side.

Front

List the side lengths in order from shortest to longest: 5, 12, 9.

Back

5, 9, 12.

Front

Do the side lengths 2, 2, and 4 form a triangle?

Back

No, because 2 + 2 = 4, which is not greater than 4.

Front

If the sides of a triangle are 7, 10, and 5, do they satisfy the Triangle Inequality Theorem?

Back

Yes, because 7 + 5 > 10, 7 + 10 > 5, and 10 + 5 > 7.

Front

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

Back

Lengths 1, 2, and 3 cannot form a triangle because 1 + 2 = 3.

Front

What is the maximum length of a side in a triangle with sides 3 and 4?

Back

The maximum length of the third side must be less than 7 (3 + 4).