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

Will the sides 3, 4, and 5 form a triangle?

Back

Yes, because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

Will the sides 1, 2, and 3 form a triangle?

Back

No, because 1 + 2 is not greater than 3.

Front

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

Back

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

Front

Which of the following sets of lengths can form a triangle: 5, 5, 10 or 5, 5, 9?

Back

5, 5, 9 can form a triangle, but 5, 5, 10 cannot.

Front

What is the minimum length of the third side if two sides of a triangle are 7 and 10?

Back

The minimum length of the third side must be greater than 3 (10 - 7).

Front

What is the maximum length of the third side if two sides of a triangle are 7 and 10?

Back

The maximum length of the third side must be less than 17 (7 + 10).

Front

Can the sides 2, 2, and 4 form a triangle?

Back

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

Front

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

Back

An example is 6, 8, and 10.

Front

If one side of a triangle is 12, what can you say about the other two sides?

Back

The sum of the other two sides must be greater than 12.