Understanding the Pythagorean Theorem

Archimedes

Euclid

Pythagoras

Aristotle

The hypotenuse is the sum of the other two sides.

The hypotenuse is the difference of the squares of the other two sides.

The square of the hypotenuse is equal to the sum of the squares of the other two sides.

The hypotenuse is twice the length of one of the other sides.

3-4-5 Triangle

Scalene Triangle

Isosceles Triangle

Equilateral Triangle

13

15

17

10

Triangles with all sides as odd numbers

Triangles with one side as a prime number

Right triangles with all sides as whole numbers

Triangles with all sides as even numbers

Divide the hypotenuse by the known leg and take the square root.

Multiply the known leg by the hypotenuse and take the square root.

Add the square of the known leg to the square of the hypotenuse and take the square root.

Subtract the square of the known leg from the square of the hypotenuse and take the square root.

7.81

8.00

7.50

8.10

3√2

√36

√9 + √2

2√9

4√11

2√44

√176

8√2

To convert the number into a fraction

To make calculations easier

To find the exact value of a number

To express the number in its simplest form