Triangle

A Triangle is the 2-simplex. The study of triangles is called trigonometry. Its Bowers acronym is "trig".

Equilateral
When all of the angles and edges of a triangle are equal a triangle is equilateral. Each angle must have a measure of exactly 60 degrees.

Isosceles
When a triangle has two equal sides, it is isosceles. It must also have two equal angles.

Scalene
A triangle with three unique side lengths is known as a scalene triangle.

Acute
A triangle with all three angles smaller than 90 degrees is called an acute triangle. All equilateral triangles are also acute triangles.

Right-Angled
A triangle with one right angle is a right-angled triangle. Their side lengths follow the equation

$$a^2 + b^2 = c^2$$ , where c is the edge length of the side opposite the right angle.

Obtuse
A triangle where at least one angle is greater than 90 degrees is called an obtuse triangle.

Special Cases
A triangle with more than one right angle is usually degenerate, but can appear on the surface of a sphere. The same applies to a triangle with angles that sum to greater than 180 degrees, and to triangles that have any angle equal to 180 degrees.