Pythagoras was an ancient Greek mathematician born around 500 BC outside of Athens. The document discusses the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the two legs. It provides examples of using the theorem to find missing side lengths of right triangles.

1. Investigating the
Pythagorean Theorem
Grade 8 Mathematics
Mr. J. Lingley

2. A Wise Man’s Theorem
leg
Pythagoras was an ancient
mathematician who was
born in 500 BC outside of
Athens Greece.
hypotenuse
leg
leg
• 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.

3. Where’s the Hypotenuse?

4. 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’

8. + =
• 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.

9. Your Turn
Find the missing side lengths.
5 cm
?
10 cm
4 cm
4 cm
?
25 cm
?
15 cm