Triangle-Sum of Angles

A quick little sketch to support students wondering why the sum of the
angles of a triangle is what it is.

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Turns out it depends on the parallel postulate! What does that mean about triangles on the sphere or in hyperbolic space? Or even in our own universe, since we're only approximately Euclidean? Dare we ask about triangles moving at relativistic speeds?

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John Golden, Created with GeoGebra