# Scalene Triangle

## Definition

Scalene triangle is a figure where no sides are of same length, and no angles are equal.

## Properties

1. No equal (congruent) sides, in ∆ABC sides AB ≠ BC ≠ CA
2. No equal angles, so ∠ABC ≠ ∠BAC ≠ ∠ACB
3. No line of symmetry
4. No point of symmetry
5. Internal angles can be an acute, obtuse or right angle, for example in ∆ABC all angles are ∠90° and thus acute
6. The smallest side is always opposite to the smallest angle, while the longest side is always opposite of the largest angle. In ∆ABC, since AB = smallest side, ∠ACB = smallest angle; similarly BC = longest side, ∠BAC = largest angle

## Types

Scalene triangles are classified into three types: 1) acute scalene triangle, 2) obtuse scalene triangle, and 3) right scalene triangles.

The differences between the types are given below:

## Formulas

The formulas for area and perimeter of a scalene triangle are the same as that of other triangles:

Area (A) = ½ (b × h), where b=base and h=height

Perimeter (P) = a + b + c, where a, b, c are the measures of three sides