Triangle Classification by Sides
Equilateral, isosceles, and scalene logic explained with examples.
By Geometry Editorial Team | 2026-06-02
Quick Answer
Side-based classification compares equality patterns among three validated side lengths.
All equal = equilateral, two equal = isosceles, all different = scalene
Table of Contents
Introduction
Use the Classifying Triangles Calculator homepage to test side sets quickly while learning side-based criteria.
This method is one of the most common entry points for geometry students.
Main Content
What is it?
Side classification only requires side lengths, but values must still form a valid triangle.
For angle-based extension, continue to Triangle Classification by Angles. For complete mixed practice, see Triangle Classification Examples.
Formula
Class labels are determined by equality count, not by side size alone.
Always run triangle inequality before assigning any label.
Step-by-step guide
- Sort or compare three side lengths.
- Check inequality conditions.
- Assign equilateral, isosceles, or scalene.
- Optionally derive angle class for fuller description.
Example
Sides 9, 9, and 12 satisfy inequality and show two equal values, so the side class is isosceles.
FAQ
Can equal sides fail to make a triangle?
Yes, if inequality fails with the third side.
Do I need angles for side classification?
No, side classification only needs valid side lengths.
Conclusion
Side-based classification is simple and powerful when paired with proper validation.
Check side sets now