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August 30, 2015

Homework Help: number theory

Posted by kay on Wednesday, January 30, 2013 at 6:44pm.

According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is their argument. Given the obtuse angle x, we make a quadrilateral ABCD with DAB = x, and ABC = 90◦, andAD = BC. Say the perpendicular bisector toDC meets the perpendicular bisector to AB at P. ThenPA = PB andPC = PD. So the trianglesPADandPBC have equal sides and are congruent. Thus PAD = PBC. But PAB is isosceles, hence PAB = PBA. Subtracting, gives x = PAD− PAB = PBC − PBA = 90◦. This is a preposterous conclusion – just where is the mistake in the “proof” and why does the

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