Triangle inequality – joining three segments

MathematicsPlane GeometryAges 12–13

Three segments a, b, c form a triangle if and only if each side is shorter than the sum of the other two. Drag the sliders or drag vertices A and C to change the lengths: when one segment is too long, the other two laid end to end still cannot meet, and the simulation shows the gap clearly. When a triangle can be formed, the angles appear so you can see the largest side facing the largest angle.