Question

prove that the difference of any two sides of a triangle is less than the third side

Answer 1

Start with the Triangle Inequality Theorem which is, the sum of any two sides of a triangle must be greater than the third. Stated algebraically: 
A < B + C 
B < A + C 
C < A + B 

1. Subtract B from both sides, then A - B < C 
2. Subtract C from both sides, then B - C < A 
3. Subtract A from both sides, then C - A < B

Answer 2

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