Pythagoras Theorem

[PiRsq]

http://www.ies.co.jp/math/java/geo/pitha1/pitha1-2.gif

This is one of the many pythagorean proofs and I dont understand why A1=A2 and A4=A3? Can someone explain this to me please?

[NateTG]

ABC, HBA, and HAC are all similar triangles.

That means that the ratio of the sides are the same/
so AB/BC=BH/AB
so AB*AB=BH*BC
so A1=A2

There is a simliar argument for B1 and B2

[PiRsq]

I see now, thanks