basic facts: triangles are assumed to be two-dimensional plane figures, unless the context provides otherwise... elementary facts about triangles were presented by euclid in books 1–4 of his elements, c. 300 bc. triangles can be classified according to the lengths of their sides. there are variations on three types:
-an equilateral triangle has all sides the same length. and it is also a regular polygon with all angles measuring 60°. (this painting contains stacked rows of smaller upright and implied inverted equilateral triangles within a larger centrally drawn equilateral triangle.)
-an isosceles triangle has two sides of equal length. and it also has two angles of the same measure, namely the angles opposite to the two sides of the same length; this fact is the content of the isosceles triangle theorem known by euclid...
-a scalene triangle has all its sides of different lengths. equivalently, it has all angles of different measure.