In this post, I’ll be writing about some peculiar properties of C squared in Pythagoras’ theorem.
Look at this diagram very carefully…
*What are the weird properties of C^2..? It turns out that A1=A2 and A3=A4. A2 + A4 = C^2.
It turns out out that area A1 is equal to area A2, and that area A3 is equal to area A4:
A1 = A2
A3 = A4
This can be proven because:
Now, due to the above:
But… B^2 is actually the area A1 and Cx is the area A2, which means that A1=A2.
Now, if B^2=Cx, this means that:
However, A^2 is equal to the area A3, and C(C-x) is equal to the area A4 – which means that A3=A4. Hence, we’ve proven that: