What is the geometric interpretation of reverse triangle inequality?

Question

In almost every book of real analysis, geometric interpretation of triangle inequality is mentioned.

But what is the geometric interpretation of reverse triangle inequality.

$$||x|-|y||\leq |x-y|$$

I know this inequality is used to show that norm function is continuous. Are there any other ways to geometrically interpret the reverse triangle inequality.

Answer 1

The length difference between any two sides of a triangle is always smaller than that of the third. Does this count?

Answer 2

I added color and vector names to Najib Idrissi's picture for more contrast and detail.

Does this help?– Najib Idrissi Apr 29 '14 at 14:02