The Pythagorean Theorem: Squares on the Sides of a Right Triangle

0:00How are the sides of a right triangle related?

0:04A right triangle has a right angle, a square corner of 90 degrees.

0:09Its sides are 3, 4 and 5 centimetres.

0:14The side across from the right angle is the hypotenuse, the longest side.

0:20The legs make the right angle: call them a and b. The hypotenuse is c.

0:27Now draw a square on each side of the triangle.

0:31The square on a has area 3 squared, 3 times 3, which is 9 square centimetres.

0:38The square on b has area 4 squared, which is 16 square centimetres.

0:45The square on c has area 5 squared, which is 25 square centimetres.

0:51Add the two smaller areas: 9 plus 16 is 25, the area of the big square.

0:58This is the Pythagorean theorem: in any right triangle, a squared plus b squared equals c squared.

1:07Now open the corner to more than 90 degrees, so the third side is 6 centimetres.

1:133 squared plus 4 squared is still 25, but 6 squared is 36.

1:2025 is not 36, so the theorem needs a right angle.

1:26Back to our right triangle: a common mistake is putting the longest side as a or b.

1:33That gives 9 plus 25, which is 34, but 4 squared is only 16.

1:40c must be the hypotenuse, the longest side: 3 squared plus 4 squared equals 5 squared.

1:48In a right triangle, a squared plus b squared equals c squared, where c is the hypotenuse.