Investigating the Pythagorean Theorem

Grade 8 Mathematics Mr. J. Lingley

A Wise Man’s Theorem

• The Pythagorean Theorem describes only the right triangle.

• In a right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares around the legs.

• The hypotenuse is always opposite of the right angle.

Pythagoras was an ancient mathematician who was

born in 500 BC outside of Athens Greece.

hypotenuse

leg

leg

leg

Where’s the Hypotenuse?

Find the length of the line segment using Pythagoras’s help.

• Using the line as the hypotenuse, complete the right angle triangle.

• Around each of the segments of the triangle, draw squares.

• Try to find the length of the ‘red line’

+ =

• The squares around the two legs = the hypotenuse. • If you know the area of the hypotenuse, then you

can find the side length by taking the square root. • if you work backwards, you can find the length of a

leg.

Your TurnFind the missing side lengths.

5 cm

10 cm

?4 cm

4 cm

?

?

25 cm15 cm