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Problem 540: Right Triangle, Square, Parallel, Perpendicular,
Dissection, Area, Pythagoras. Level: High School, SAT Prep, College
The figure shows a right triangle ACB with
the squares ABDE, ACJK (area A1), and BCMN (area A2). AG and DH are parallel to line CBF. Line EHG and DF are parallel
to AC. If A3 is the area of the
region ACFDHG, prove that A1 + A2 = A3.
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