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Mathematics, 20.06.2019 18:04
Here is their argument. given the obtuse angle x, we make a quadrilateral abcd with ā dab = x, and ā abc = 90ā¦, and ad = bc. say the perpendicular bisector to dc meets the perpendicular bisector to ab at p. then pa = pb and pc = pd. so the triangles pad and pbc have equal sides and are congruent. thus ā pad = ā pbc. but pab is isosceles, hence ā pab = ā pba. subtracting, gives x = ā padāā pab = ā pbc āā pba = 90ā¦. this is a preposterous conclusion ā just where is the mistake in the "proof" and why does the argument break down there?
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