Geometry

Forgetting the Triangle Inequality

Students assume any three side lengths can make a triangle.

Quick check

Why students make it

They picture the sides as separate pieces and forget that the two shorter sides must actually meet. They may also use ≥\ge instead of the required strict inequality.

The rule done right

For three positive side lengths to make a triangle, the sum of any two sides must be greater than the third side. It is enough to check that the two shorter sides add to more than the longest side.

Related resources

trianglesinequalitiesside-lengths