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 a right triangle?

Back

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

Front

In the Pythagorean Theorem, which side is the hypotenuse?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If you know the lengths of two sides of a right triangle, how can you find the length of the third side?

Back

You can use the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

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

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5 cm.

Front

What do you do if you need to find a missing leg of a right triangle?

Back

You subtract the square of the known leg from the square of the hypotenuse: a² = c² - b².

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 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 a triangle has sides of lengths 5 cm, 12 cm, and 13 cm, is it 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 a leg if the hypotenuse and one leg are known?

Back

The formula is: a = √(c² - b²), where c is the hypotenuse and b is the known leg.