pythagoras justification

when shapes are similar their areas are in proportion to the squares of corresponding sides

drop a perpendicular from the apex at the right angle to form two similar triangles (relatively straightforward to justify) which are similar to the original triangle

k(5^2) = k(4^2) + k(3^2)
and this generalises...

not that helpful as a means of justifying the theorem maybe, but a neat enough way of tying in the area property of similar shapes

[ from the website betterexplained ]