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?
1 answer
It is advised to not cheat on the PROMYS application problems. If you are stuck on one then try another one.