Classifying Triangles Calculator
Classify triangles by sides (equilateral, isosceles, scalene) and angles (acute, right, obtuse)
Triangle Classification
Example Classifications
Equilateral Triangle
Sides: a = 5, b = 5, c = 5
Angles: A = 60°, B = 60°, C = 60°
Classification: Equilateral (all sides equal, all angles 60°)
Right Isosceles Triangle
Sides: a = 5, b = 5, c = 7.07
Angles: A = 45°, B = 45°, C = 90°
Classification: Right Isosceles (two equal sides, one 90° angle)
Obtuse Scalene Triangle
Sides: a = 3, b = 4, c = 6
Angles: A = 26.4°, B = 41.4°, C = 112.2°
Classification: Obtuse Scalene (all sides different, one angle > 90°)
Classification Guide
By Sides
By Angles
Quick Tips
Triangle inequality: Sum of any two sides > third side
All angles in a triangle sum to 180°
Equilateral triangles are always acute (60° each)
A triangle can be both isosceles and right
Understanding Triangle Classification
Classification by Sides
Triangles are classified by their side lengths based on how many sides are equal:
Equilateral Triangle
All three sides are equal in length. All angles are also equal (60° each).
Isosceles Triangle
Exactly two sides are equal. The angles opposite the equal sides are also equal.
Scalene Triangle
All three sides are different lengths. All angles are also different.
Classification by Angles
Triangles are also classified by their largest angle:
Acute Triangle
All three angles are less than 90°. This type appears "sharp" or "pointed".
Right Triangle
One angle is exactly 90°. The side opposite the right angle is the hypotenuse.
Obtuse Triangle
One angle is greater than 90°. This type appears "wide" or "blunt".
Important Properties
Triangle Inequality Theorem
For any triangle with sides a, b, and c:
- • a + b > c
- • a + c > b
- • b + c > a
Angle Sum Property
The sum of all interior angles in any triangle is always 180°:
∠A + ∠B + ∠C = 180°