Understanding Triangle Inequality

According to triangle inequality, given the triangle with side lengths A, B, and C (from smallest to largest), C must be less than the sum of A and B. This is what gives me the maximum.

However, I also found that the minimum is not simply the smallest length (A) but the difference between A and B, according to the quizzes I've been doing. Why is that?

I can't seem able to get from C < A + B to C > B - A algebraically to prove this.

Note by Ryan Huynh
9 months, 2 weeks ago

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Since the triangle inequality theorem applies to all sides this means that B<C+AB<C+A.

If we subtract AA from both sides, we get BA<CB-A<C or C>BAC>B-A

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