Pythagorean Theorem

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). It is expressed as c² = a² + b².

Front

What are the legs of a right triangle?

Back

The legs of a right triangle are the two sides that form the right angle. They are usually referred to as sides a and b.

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the side opposite the right angle in a right triangle and is always the longest side.

Front

If a = 3 and b = 4, what is c?

Back

Using the Pythagorean Theorem: c² = a² + b²; c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

Do the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

What is the formula to find the length of the hypotenuse?

Back

The formula to find the length of the hypotenuse (c) is c = √(a² + b²).

Front

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

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

If c = 10 and a = 6, what is b?

Back

Using the Pythagorean Theorem: b² = c² - a²; b² = 10² - 6²; b² = 100 - 36; b² = 64; b = 8.

Front

What does it mean if a triangle does not satisfy the Pythagorean Theorem?

Back

If a triangle does not satisfy the Pythagorean Theorem, it is not a right triangle.

Front

Can the lengths 7, 24, and 25 form a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, which is equal to 25².