Scalene triangle definition - Math Open Reference

Scalene Triangle

From Greek: skalenos - "uneven, unequal"

A triangle where all three sides are different in length.

Try this Drag the orange dots on each vertex to reshape the triangle. Try to establish a triangle that is not scalene. Sometimes called an irregular triangle.

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Scalene triangles are unusual in that the are defined by what they are not. Most triangles drawn at random would be scalene. The interior angles of a scalene triangle are always all different. The converse of this is also true - If all three angles are different, then the triangle is scalene, and all the sides are different lengths.

Scalene Triangle Facts

Interior angles are all different	In the figure above, drag any vertex and see that this is always true. To see why this is so, imagine two angles are the same. The triangle would then be an Isosceles triangle, which has two sides the same length. Similarly, if all three angles are the same, it would be an equilateral triangle and all three sides would be the same length. See the entries for Isosceles and Equilateral triangles.
Shortest side is opposite the smallest angle	For more on this see Side / angle relationship in a triangle
Longest side is opposite the largest angle	For more on this see Side / angle relationship in a triangle

Area of a scalene triangle

Since in a scalene triangle you probably know the lengths of all three sides, the best way to calculate the area is using Heron's Formula. However you can use any method that works with what you are given. See Area of a Triangle

Related triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises