How do we define the pythagorean theorem without diagrams or pictures?

The Pythagorean Theorem describes the relationship in Euclidean Geometry between the three sides of any right triangle.

Definitions:

Right triangle – a triangle with a right angle

Hypotenuse – longest side of a right triangle, opposite the right angle

Legs of a right triangle – the two sides opposite the two acute angles

In any right triangle, the area of the square whose side is the length of the hypotenuse of the right triangle is equal to the sum of the two areas of the squares whose sides are the lengths of the two legs.

In the below diagram, the legs of the triangle are AB and CB, and the hypotenuse is AC. If you add the area of the squares adjacent to AB and CB together, the total will equal the area of the square adjacent to AC.