Pythagorean Theorem: Explaining A1=A2 & A4=A3

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SUMMARY

The discussion focuses on the Pythagorean Theorem, specifically the proof involving similar triangles ABC, HBA, and HAC. The key conclusion is that the equality A1=A2 and A4=A3 is derived from the similarity of these triangles, leading to the ratio of sides being consistent. The mathematical relationship is established through the equation AB/BC=BH/AB, which simplifies to AB²=BH*BC, confirming the equality of areas A1 and A2.

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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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