Triangle Inequality Theorem Converse

A triangle cannot be constructed from three line segments if any of them is longer than the sum of the other two.
Try this Drag any orange dot. Notice you cannot make a triangle out of these three segments.

In the above figure, the lengths of the sides A and B add up to less than the length of C. This violates the Triangle Inequality Theorem, and so it is not possible for the three lines segments to be made into a triangle. In the figure above, drag both loose ends down on to the line segment C, to see why this is so.

[Thanks to Jeff Holcomb, Santa Cruz City Schools, California for the inspiration for the above applet]

Other triangle topics


Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises