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This 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 pa
by lloeki 2y ago
This 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.