How do you show that Pythagoras theorem is real?

Answer 1

Draw a square, side length a. INSIDE the square, on each side of the square, draw a right-angled triangle, all 4 being exactly the same shape. That will leave you with a small square in the middle, side length b. Give name letters c and d to the remaining short and long sides of the triangles. Now use the fact that the total area of the 4 triangles plus the area of the little square add up to the area of the big square, and secondly that d=c+b, and you will discover Pythagoras' result.

Another way is to draw a right-angled triangle and then draw a line from the right-angle-corner perpendicular to the opposite side (the hypotenuse). You now have 3 triangles of identical shape. Therefore the ratios of the corresponding sides in each triangle are equal. From this you can also prove the Pythagoras theorem.