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.
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Click image to the left for more content.CK-12 Foundation: Chapter5TriangleInequalityTheoremA
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Click image to the left for more content.James Sousa:Triangle InequalityTheorem
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.
Example A
Do the lengths 4, 11, 8 make a triangle?
To solve this problem, check to make sure that the smaller two numbers add up to be greater than the biggest number.
4 + 8 =12 and 12>11 soyesthese lengths make a triangle.
Example B
Find the length of the third side of a triangle if the other two sides are 10 and 6.