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 the argument break down th

Answer 1

Hmmm... drawing...

Answer 2

Perpendicular bisector to DC

Answer 3

I still have no idea... TL;DR ?

Answer 4

If only I could draw better :>

Answer 5

the drawing isn't exact, but it's more finished