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]
Other triangle topics
Perimeter / Area
Congruence and Similarity
Triangle quizzes and exercises
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