Types of Triangles
A clear guide to equilateral, isosceles, scalene, acute, right, and obtuse triangles.
By Geometry Editorial Team | 2026-06-02
Quick Answer
Triangles are classified by side equality and by angle size, and one triangle can belong to both systems at once.
Angle classes use the largest angle: acute < 90, right = 90, obtuse > 90
Table of Contents
Introduction
Visit the Classifying Triangles Calculator homepage first if you want to test these triangle types with real values while reading.
Knowing triangle types makes every geometry chapter easier, from basic shape identification to proofs and applications.
Main Content
What is it?
Side-based types are equilateral, isosceles, and scalene. Angle-based types are acute, right, and obtuse.
If you need detailed side logic, continue with Triangle Classification by Sides. For angle-focused reasoning, read Triangle Classification by Angles.
Formula
For angle categories, evaluate the largest interior angle after validating total angle sum.
For side categories, compare side lengths directly and ensure inequality rules are satisfied.
Step-by-step guide
- Determine whether side data or angle data is available.
- Apply side or angle rules to find the primary class.
- Add a secondary class when enough data exists.
- Write the final type clearly for reporting or grading.
Example
A triangle with angles 90, 45, and 45 is right by angle and isosceles by equal angle implication.
A triangle with sides 4, 5, and 6 is scalene by sides and often acute by angle behavior.
FAQ
Can a triangle be both right and isosceles?
Yes. A 45-45-90 triangle is a common example.
Is equilateral also acute?
Yes, because all angles are 60 degrees.
Conclusion
Understanding triangle types helps you move from measurement data to reliable geometric conclusions.
Classify a triangle now