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As the article mentions, in this particular case it's simpler: You have a point on the triangle that is also on the circle. Now you rotate the triangle 180 degr
by vidarh 2y ago
As the article mentions, in this particular case it's simpler: You have a point on the triangle that is also on the circle. Now you rotate the triangle 180 degrees, with the point following the circle. The point inherently must end up exactly opposite the original point, and so the diagonal formed between the old and new point must be the diameter of the circle.
- lloeki 2y agoThis proves that the parallelogram diagonals, both being diameters of the same circle, are equal, akho was pointing out that there's a leap from that to "the parallelogram is a rectangle", which can be proven with Thales. But then, the article is about laying out a proof of Thales so if it's using a lemma that leveraged Thales itself that's circular logic right there and so we're in trouble. One other way to prove Thales is by computing angles, but then you've got yourself a proven Thales so the point of the article is moot.
- vidarh 2y agoI didn't read that very carefully, but proving that a parallelogram with equal diagonals is a rectangle is obvious enough via triangle congruency that I suspect they were just taught it without the proof. It's not a particularly interesting detail.