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

Equilateral: All three sides equal
Isosceles: Two sides equal
Scalene: All sides different

By Angles

Acute: All angles < 90°
Right: One angle = 90°
Obtuse: One angle > 90°

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°