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KK.2 Equilateral, isosceles, and scalene triangles

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What are Equilateral, Isosceles, and Scalene Triangles?

Triangles are classified by their side lengths into three main categories: equilateral, isosceles, and scalene.

Examples:
  • An equilateral triangle has all three sides equal in length
  • An isosceles triangle has at least two sides equal in length
  • A scalene triangle has all three sides different lengths
Note

Think of triangle classification as a way to organize triangles based on how many sides have the same length.

Equilateral Triangles

An equilateral triangle has all three sides exactly the same length and all three angles equal to 60°.

Characteristics:
  • All three sides are congruent (equal length)
  • All three angles measure exactly 60°
  • It has three lines of symmetry
  • It has rotational symmetry of order 3
Note

The word "equilateral" comes from "equi-" meaning equal and "lateral" meaning sides. All equal sides!

Isosceles Triangles

An isosceles triangle has at least two sides of equal length, called legs, and a third side called the base.

Characteristics:
  • Two sides are equal in length (the legs)
  • The angles opposite the equal sides are also equal
  • It has one line of symmetry
  • It may have two acute angles and one different angle
Note

All equilateral triangles are also isosceles triangles, but not all isosceles triangles are equilateral.

Scalene Triangles

A scalene triangle has all three sides of different lengths and all three angles of different measures.

Characteristics:
  • No sides are equal in length
  • No angles are equal in measure
  • It has no lines of symmetry
  • All three interior angles are different
Note

Most triangles you see in everyday life are scalene triangles, like many roof trusses and sailboat sails.

Identifying Triangle Types by Side Lengths

To classify a triangle by its sides, measure or compare the lengths of all three sides.

Identification Steps:
  • Measure all three sides of the triangle
  • Compare the side lengths:
    • If all three sides are equal → Equilateral
    • If exactly two sides are equal → Isosceles
    • If all three sides are different → Scalene
Note

When measuring sides, be precise! Even a small difference in length can change a triangle's classification.

Real-World Examples of Triangle Types

Different types of triangles are used in various structures and designs based on their properties.

Examples:
  • Equilateral: Yield traffic signs, some pizza slices, certain architectural details
  • Isosceles: The pediment of ancient Greek temples, many roof trusses, some sandwich halves
  • Scalene: Most irregular-shaped plots of land, many sailboat sails, random triangular objects
Note

Engineers and architects choose specific triangle types for structures based on the strength and stability needed.

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