Question

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