Triangle Inequality and Pythagorean 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

Given sides a, b, and c, what must be true for a triangle to exist?

Back

The conditions a + b > c, a + c > b, and b + c > a must all be satisfied.

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².

Front

Can a triangle have sides of lengths 15, 12, and 9?

Back

Yes, because 15 < 12 + 9, 12 < 15 + 9, and 9 < 15 + 12.

Front

Which side length would NOT work to form a triangle with sides 2 and 6?

Back

4, because 2 + 6 > 4, but 6 + 4 > 2 and 2 + 4 > 6.

Front

How can you determine if a triangle is a right triangle?

Back

Use the Pythagorean Theorem: if a² + b² = c² holds true, then the triangle is a right triangle.

Front

What is the maximum length of the third side of a triangle with sides 5 and 5?

Back

The maximum length is less than 10 (5 + 5), but greater than 0 (5 - 5). A possible length is 9.

Front

Can the sides of a triangle have lengths 3, 8, and 9?

Back

Yes, because 3 + 8 > 9, 3 + 9 > 8, and 8 + 9 > 3.

Front

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

Back

The lengths 1, 2, and 3 cannot form a triangle because 1 + 2 is not greater than 3.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the length of the hypotenuse is always the longest side.