right triangle - has one 90° angle
Pythagorean triangle - right triangle whose side lengths are all integers
oblique triangle - has no 90° angle
acute triangle - each angle is less than 90°
obtuse triangle - one angle is greater than 90°
equilateral triangle - angles are 60°-60°-60°
isosceles triangle - has two equal angles
scalene triangle - has three different angles
rational triangle - all side lengths are rational
integer triangle - all side lengths are integers
Heronian triangle - all side lengths and area are integers
equable triangle - has a perimeter of n units and and area of n square units
degenerate triangle - angles are 0°-0°-180°
planar triangle - a triangle drawn on a flat surface (plane)
non-planar triangle - a triangle drawn on a curved surface
spherical triangle - a non-planar triangle on a convex surface, like the Bermuda Triangle
hyperbolic triangle - a non-planar triangle on a concave surface
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