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.
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]
While you are here..
... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone.
However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site?
When we reach the goal I will remove all advertising from the site.
It only takes a minute and any amount would be greatly appreciated.
Thank you for considering it! – John Page
Become a patron of the site at patreon.com/mathopenref
Other triangle topics
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
(C) 2011 Copyright Math Open Reference. All rights reserved