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 15, 12, and 9, does it satisfy the Triangle Inequality Theorem?

Back

Yes, because 15 < (12 + 9), 12 < (15 + 9), and 9 < (15 + 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 7, 7, and 19 form a triangle?

Back

No, because 7 + 7 is not greater than 19.

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 three lengths that can form a triangle?

Back

Lengths 3, 4, and 5 can form a triangle because 3 + 4 > 5, 3 + 5 > 4, and 4 + 5 > 3.

Front

What is the maximum length of one side of a triangle if the other two sides are 8 and 6?

Back

The maximum length is less than 14 (8 + 6).

Front

If a triangle has sides of lengths 3, 5, and 5, does it satisfy the Triangle Inequality Theorem?

Back

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

Front

What happens if the sum of two sides of a triangle equals the third side?

Back

The three points are collinear, and they do not form a triangle.

Front

What is the minimum length of one side of a triangle if the other two sides are 10 and 5?

Back

The minimum length must be greater than 5 (10 - 5).