How can we best describe and represent Pythagorean Theorem in geometry?

Answer 1

I agree draw some on graph paper. This will show it work for many, but the most important fact is it works for all right triangles.

Answer 2

The sum of the squares of the legs of the right triangle equals the square of the hypotenuse

The proof is done by appealing to the trig identity sin^2 t+ cos^2 t= 1

Draw the following triangles on graph paper, and then complete the table

leg #1 leg #2 hypotenuse leg#1^2 leg#2^2 leg1^2+ leg2^2 hypotenuse^2

5 12 13 25 144 169 169

3 4 5 9 16 25 25

7 24 25

8 15 17

compare the last two columns

I am sure there are plenty more ways to appeal to the Visual and kinesthetic learner...