Triangles are three-sided shapes formed by joining three non-collinear points. Triangles can be classified based on their angles as acute, right, or obtuse triangles, or based on their sides as equilateral, isosceles, or scalene triangles. An acute triangle has all angles less than 90 degrees, a right triangle has one 90 degree angle, and an obtuse triangle has one angle greater than 90 degrees. An equilateral triangle has all three sides the same length, an isosceles triangle has two sides the same length, and a scalene triangle has no sides the same length.