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Introduction to :

A long time ago, in ancient Greece, a brilliant guy named Pythagoras discovered something pretty amazing and useful.

Pythagorean Theorem: a2 + b2 = c2

In a right triangle the sum of the squares of the two legs equals the square of the hypotenuse.

Pythagorean abc

  • Legs (a and b): the sides of the triangle adjacent to the right angle. They don't need to be the same length in order for this theorem to work
  • Hypotenuse (c): the side of the triangle opposite the right angle

Right Triangles

So, let's break this down. If you square each side of the triangle, the sum of the areas of the two legs squared is equal to the hypotenuse squared.

Pythagorean Image

Here you can see it with numbers:

Pythagorean with numbers

The area of the two smaller squares is 3 x 3 = 9 cm^2 and 4 x 4 = 16cm^2

The area of the larger square is equal to 5 x 5 = 25 cm^2

If you add the two smaller areas together, you get the area of the square of the hypotenuse 9 + 6 = 25 cm^2

Look Out: Do not attempt this with obtuse or acute triangles! This awesome theorem only works for right triangles!

Example 1

Find the missing side of this triangle.

Triangle

The length of the hypotenuse is missing, and we are given the lengths of the legs.


Example 2

Find the length of the missing side of this right triangle.

Right triangle

The length of a leg is missing, and we are given the lengths of the other leg and the hypotenuse.


Example 3

Is a triangle with sides lengths of 4 cm, 7 cm, and 8 cm a right triangle?

If it is a right triangle, then the sum of the squares of the two smaller sides will equal the square of the largest side.


Exercise 1

Find the length of the missing side of this triangle.

4 x 3 Triangle

Exercise 2

Find the length of the missing side of this triangle.

41 x 9 Triangle

Exercise 3

Could a right triangle have side lengths of 29, 21, and 20 inches?

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