Spherical Triangle: Sum of Two Sides is Always Bigger than Third Side

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prinsinn
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Do you know any good example (or proof) that shows that the sum of two sides is alwasys bigger than the third side in a spherical triangle.
 

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How about simply "a straight line is the shortest distance between two points"?
 
Think about the converse. What is a triangle like when the third side is equal to or less then the 2 other sides put together?
 

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