Geometry Problem

Click the figure below to see the complete problem 540 about Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras.

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## Tuesday, November 9, 2010

### Problem 540: Right Triangle, Square, Parallel, Perpendicular, Dissection, Area, Pythagoras

Labels:
area,
dissection,
parallel,
perpendicular,
Pythagoras,
right triangle,
square

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Denote length AC = b, length BC = a (assume a>b)

ReplyDeleteExtend NB to meet HD at X;

Extend AG to meet BX at Y.

Easy to derive GH = HX = a - b,

XD = BF = b,

DF = XB = a,

A3 = Area of rectangle ACBY

+ Area of rectangle BFDX

+ Area of square GHXY

= ab + ab + (a-b)^2

= a^2 + b^2

= A1 + A2