A triangle is a 3-sided polygon with three sides, three vertices, and three angles. Triangles can be categorized based on their side lengths as either equilateral (all sides equal), isosceles (two sides equal), or scalene (no sides equal). They can also be categorized based on their angle measures as either acute (all angles less than 90 degrees), obtuse (one angle greater than 90 degrees), or right (one angle of 90 degrees). The study of triangles, known as triangle geometry, contains many beautiful theorems and relationships.