Frequently Asked Questions
What is the triangle inequality?
For three side lengths to form a triangle, the sum of any two must be strictly greater than the third. Equivalently, the largest side must be less than the sum of the other two.
What happens if equality holds?
If the sum equals the third side, the three points are collinear - a degenerate (flat) triangle with zero area.
Does the inequality extend to higher dimensions?
Yes - it is the defining property of a metric space. For any three points a, b, c the distance from a to c is at most the sum of distances from a to b and b to c.
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