The document defines and describes the different types of triangles based on their angles and sides. It states that a triangle is a three-sided polygon with three angles and vertices. Triangles are categorized as being right, acute, or obtuse angled based on whether they have one 90 degree angle, all angles less than 90 degrees, or one angle greater than 90 degrees. They are also defined as being scalene, isosceles, or equilateral based on whether their sides are all different lengths, two sides are the same length, or all three sides are the same length respectively.