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The perpendicular bisector of the line joining

 
 

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2.According to the Journal of Irreproducible Results, any obtuse angle is a right angle! x A P B C D Here is their argument. Given the obtuse ...

C D Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with ∠DAB = x, and ∠ABC = 90◦ , and AD = BC. Say the perpendicular bisector to DC meets the perpendicular bisector to AB at P. Then P A = P B and P C = P D. So the triangles P AD and P BC have equal sides and are congruent. Thus ∠P AD = ∠P BC. But P AB is isosceles, hence ∠P AB = ∠P BA. Subtracting, gives x = ∠P AD − ∠P AB = ∠P BC − ∠P BA = 90◦ . This is a preposterous conclusion – just where is the mistake in the “proof” and why does the argument break down there?
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1.AU MAT 120 Systems of Linear Equations and Inequalities Discussion

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