http://www.ck12.org Chapter 5. Relationships with Triangles
5.7 Triangle Inequality Theorem
Here you’ll learn the Triangle Inequality Theorem, which will help you to determine whether three side lengths will
create a triangle or not.
What if you had to determine whether the three lengths 5, 7 and 10 make a triangle? After completing this Concept,
you’ll be able to use the Triangle Inequality Theorem to determine if any three side lengths make a triangle.
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/52531CK-12 Foundation: Chapter5TriangleInequalityTheoremA
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/1291James Sousa: Triangle Inequality Theorem
Guidance
Can any three lengths make a triangle? The answer is no. There are limits on what the lengths can be. For example,
the lengths 1, 2, 3 cannot make a triangle because 1+ 2 =3, so they would all lie on the same line. The lengths 4, 5,
10 also cannot make a triangle because 4+ 5 =9.
The arc marks show that the two sides would never meet to form a triangle. TheTriangle Inequality Theorem
states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third.