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Why is SAS (Side-Angle-Side) Congruency holds true on a plane but not on a sphere? I am trying to understand why it is so (instead of proving/disproving the same). Please help me understand.

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    What's your definition of a triangle? Must all the sides be length minimizing geodesics? Are you allowed to have angles of $\pi$ radians?2012-07-08
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    I agree with @JasonDeVito, this is a question that cannot be answered without a clear definition of triangle, and is noted in some of the answers below. And I want to emphasize that there is not an obvious choice here. Different definitions will yield different answers.2016-11-08

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