Geometric Discoveries

Found on the floor of Kian's bedroom: a lined paper with the following information.  It looked interesting to me, so I picked it up and read it.  "What is this, Kian?" I asked him.  "Oh, I've been using my ruler to learn about triangles and squares."

Is he a future scientist or what?!

Triangles, squares and circles

laws I have found

1. a right triangle's hypotenuse is directly proportional to its other sides.

if Lx and Ly increase by one, its Hypotenuse increases by 1.4

(here is drawn a triangle with sides labeled H, Lxy, Lyx)

2. adding on to the first law, some triangle's hypotenuses = their other side length x 1.4

(here is a triangle with sides labeled H, Ly, Lx)

H = Lx * 1.4 but only if Lx = Ly

3. when a square with a triangle inside increases by 1, then

(here is a square with a diagonal line across it splitting it into two triangles, the sides each labeled L)

T.P = 3.4
T.A = ( (L-1) + 0.5)

I found his protractor today which somehow made it's way onto Felicity's bed and he was so excited to continue explorations which could now include angles!