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Britannica Sources used in this answer

How are triangles classified by side lengths?

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Map of the Greco-Roman world highlighting the birthplaces of notable ancient mathematicians, marked with the pi symbol and labeled with their names. Cities such as Athens, Alexandria, Syracuse, and Miletus are shown around the Mediterranean, with modern country boundaries outlined. An inset provides detail for the region of Greece and western Anatolia.
geometry This map spans a millennium of prominent Greco-Roman mathematicians, from Thales of Miletus (c. 600 bce) to Hypatia of Alexandria (c. 400 ce).

In geometry, triangles are classified by their side lengths into three distinct categories:1

  • Equilateral triangles: These have three sides of equal length.21
  • Isosceles triangles: These have exactly two sides of equal length.31
  • Scalene triangles: These have three sides of unique lengths.1

These classifications are fundamental to understanding the properties of triangles within Euclidean geometry.1