Pythagorean Theorem and Converse

Front

What is the Pythagorean Theorem?

Back

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). Formula: a² + b² = c².

Front

What is the longest side of a right triangle called?

Back

Hypotenuse.

Front

How can you determine if a triangle is acute, obtuse, or right using side lengths?

Back

Use the Pythagorean Theorem: If a² + b² > c², it's acute; if a² + b² = c², it's right; if a² + b² < c², it's obtuse.

Front

What are the side lengths of a right triangle?

Back

The two shorter sides are called legs, and the longest side is the hypotenuse.

Front

If a triangle has sides of lengths 4, 5, and 6, what type of triangle is it?

Back

Acute triangle.

Front

If a triangle has sides of lengths 2, 12, and 13, what type of triangle is it?

Back

Obtuse triangle.

Front

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

Back

The sum of the squares of the two legs equals the square of the hypotenuse.

Front

What is the formula to find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) for a leg.

Front

What does it mean if a triangle is classified as 'not a triangle'?

Back

The side lengths do not satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the triangle inequality theorem?

Back

For any triangle with sides a, b, and c: a + b > c, a + c > b, and b + c > a.