# rectangles1 - (4) any right triangle has defect=0 (5) there...

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Math402 Defects and Rectangles Defect of an n -gon is ( n - 2) · 180 minus the sum of interior angles of the n -gon. A rectangle is a quadrilateral with all four angles equal to 90 . In particular the defect of a rectangle is 0. Theorem. The following statements are equivalent in neutral geometry: (1) Playfair (2) any triangle has defect=0 ( i.e. angle sum 180 ). (3) any polygon has defect=0
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Unformatted text preview: (4) any right triangle has defect=0 (5) there is a rectangle of any size (6) there is a rectangle (7) there is a right triangle with defect=0 (8) there is a triangle with defect=0 If any (thus all) of the above is true then we are doing Euclidean Geometry, if any (thus all) is false then we are doing Hyperbolic Geometry....
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## This note was uploaded on 08/08/2009 for the course MATH 1 taught by Professor Malkin during the Spring '09 term at University of Illinois at Urbana–Champaign.

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