The Triangle Inequality

Shortcuts and reflections

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Triangle inequality: $PR \le PQ + QR$.
• Reflecting a point turns a bent path into a straight one.
• Three lengths form a triangle when the two shorter ones sum to more than the longest.

Steps

1. The straight path
2. Heron’s river problem
3. Can it be a triangle?
4. Vectors too
5. Via the shore
6. Possible third sides