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According to the Journal of Irreproducible Results, any obtuse angle is a right angle! Here is their argument. Given the obtuse...Asked by Jewel
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 argument break down
there?
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 argument break down
there?
Answers
Answered by
Bear
It is advised to not cheat on the PROMYS application problems. If you are stuck on one then try another one.
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