5.7. Triangle Inequality Theorem http://www.ck12.org
The Triangle Inequality Theorem can also help you find the range of the third side. The two given sides are 6 and 10,
so the third side,s, can either be the shortest side or the longest side. For examplescould be 5 because 6+ 5 >10.
It could also be 15 because 6+ 10 >15. Therefore, the range of values forsis 4<s<16.
Notice the range is no less than 4, andnot equalto 4. The third side could be 4.1 because 4. 1 + 6 >10. For the
same reason,scannot be greater than 16, but it could 15.9, 10+ 6 > 15 .9.
Example C
The base of an isosceles triangle has length 24. What can you say about the length of each leg?
To solve this problem, remember that an isosceles triangle has two congruent sides (the legs). We have to make sure
that the sum of the lengths of the legs is greater than 24. In other words, ifxis the length of a leg:
x+x> 24
2 x> 24
x> 12Each leg must have a length greater than 12.
Watch this video for help with the Examples above.
MEDIA
Click image to the left for more content.CK-12 Foundation: Chapter5TriangleInequalityTheoremB
Concept Problem Revisited
The three lengths 5, 7, and 10 do make a triangle. The sum of the lengths of any two sides is greater than the length
of the third.
Vocabulary
Anisosceles triangleis a triangle with two congruent sides. The congruent sides are called thelegsand the third
side is called thebase. TheTriangle Inequality Theoremstates that to make a triangle, two sides must add up to
begreaterthan the third side.
Guided Practice
Do the lengths below make a triangle?
- 4.1, 3.5, 7.5
- 4, 4, 8
- 6, 7, 8
Answers: