I was under the impression that public FB posts were more widely visible; if not, my apologies.
Yeah, there are further implications. A lot of the classes of triangles that this methodology points to can be characterized by "such and such a line is parallel to BC", and also by relations of the form k a^2 = b^2 + c^2. Or, again, isosceles triangles can be characterized by the fact that the symmedian trail passes through the apex; the fact that the symmedian trail of a mediosimilar triangle is parallel to BC is a reflection of the "sibling" relation I spoke of. So, yeah, there's a lot more going on. But it's interesting, I think, that the characterizations I listed are so different on the surface but equivalent underneath.
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Date: 2019-02-11 01:35 am (UTC)Yeah, there are further implications. A lot of the classes of triangles that this methodology points to can be characterized by "such and such a line is parallel to BC", and also by relations of the form k a^2 = b^2 + c^2. Or, again, isosceles triangles can be characterized by the fact that the symmedian trail passes through the apex; the fact that the symmedian trail of a mediosimilar triangle is parallel to BC is a reflection of the "sibling" relation I spoke of. So, yeah, there's a lot more going on. But it's interesting, I think, that the characterizations I listed are so different on the surface but equivalent underneath.