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.

#Geometry

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Comments

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

If we subtract $A$ from both sides, we get $B-A<C$ or $C>B-A$

Δrchish Ray - 1 year, 11 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$