Triangle geometry is a branch of mathematics that focuses on the properties and relationships of triangles, which are three-sided polygons. Triangles can be classified based on their angles as acute, right, or obtuse, and based on their sides as equilateral, isosceles, or scalene. The sum of the interior angles of any triangle is always 180 degrees. Key concepts in triangle geometry include the Pythagorean theorem, which relates the lengths of the sides in right triangles, and the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side. These principles are essential for solving various geometric problems involving triangles.