Triangle Inequality
The triangle inequality states that for any triangle, the length of any one side of the triangle must be less than the sum of the lengths of the other two sides.

In other words, if you have a triangle with sides a, b, and c, then a + b > c, b + c > a, and c + a > b.
A step-by-step guide to Using Triangle Inequality Rules
For example, if you have a triangle with sides of lengths 4, 5, and 7, you can check whether it satisfies the triangle inequality:
- 4 + 5 > 7 (true)
- 5 + 7 > 4 (true)
- 7 + 4 > 5 (true)
Since all three conditions are true, this triangle satisfies the triangle inequality and is a valid triangle.
On the other hand, if you have sides of lengths 2, 5, and 10:
- 2 + 5 > 10 (false)
- 5 + 10 > 2 (true)
- 10 + 2 > 5 (true)
In this case, the first condition is false, which means that these side lengths do not form a valid triangle.
Triangle Inequality – Example 1
Do the given sides form a triangle? \(a=3, b=5, c=8\)
Solution:
Add the first and second lengths. \(3+5=8\)
8 is equal to the third length. So, it is not a triangle.
Triangle Inequality – Example 2
Do the given sides form a triangle? \(a=7, b=6, c=12\)
Solution:
Add the first and second lengths. \(7+6=13\)
13 is larger than the third length (12). So, they form a triangle.
Related to This Article
More math articles
- FREE 4th Grade FSA Math Practice Test
- 6th Grade MAAP Math Worksheets: FREE & Printable
- How to Prepare for the AFOQT Math Test?
- How to Unlock the Path to Success: “TExES Core Subjects Math for Beginners” In-Depth Solution Manual
- Dollars and Sense: How to Tackle Money Word Problems with Confidence
- The Ultimate 6th Grade PARCC Math Course (+FREE Worksheets)
- SSAT Upper-Level Math Formulas
- Begin a Captivating Journey with “ATI TEAS 7 Math for Beginners”: The Ultimate Guide and Solutions Handbook
- 4th Grade PSSA Math Worksheets: FREE & Printable
- Math Courses Required For A Business Degree
What people say about "Triangle Inequality - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.