Pythagorean Theorem: Explaining A1=A2 & A4=A3

AI Thread Summary
The discussion focuses on understanding the equality A1=A2 and A4=A3 in the context of a Pythagorean theorem proof involving similar triangles. It highlights that triangles ABC, HBA, and HAC are similar, leading to proportional relationships among their sides. The ratio AB/BC equals BH/AB, resulting in the equation AB²=BH*BC, which confirms A1=A2. A similar reasoning applies to the segments B1 and B2, clarifying the relationships further. The explanation emphasizes the importance of triangle similarity in deriving these equalities.
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http://www.ies.co.jp/math/java/geo/pitha1/pitha1-2.gif

This is one of the many pythagorean proofs and I don't understand why A1=A2 and A4=A3? Can someone explain this to me please?
 
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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
 
I see now, thanks
 

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