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 can be expressed as: c² = a² + b².

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

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

Front

True or False: To find a leg of a right triangle, you add a² + b², then square root.

Back

False. To find a leg, you subtract the square of the known leg from the square of the hypotenuse: a² = c² - b².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

If the hypotenuse is 10 and one leg is 6, what is the length of the other leg?

Back

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

Front

What does 'leg' refer to in a right triangle?

Back

A leg refers to either of the two sides that form the right angle in a right triangle.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem only applies to right triangles.

Front

What is the formula to find the hypotenuse in a right triangle?

Back

The formula is c = √(a² + b²), where c is the hypotenuse and a and b are the legs.

Front

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

Back

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