Euclidean geometry, is simply plane and solid geometry. It is named after the Greek mathematician, Euclid, when he proposed his five postulates which serve as basis of drawing plane and solid figures. So, in a nutshell, a triangle in Euclidean geometry is a two-dimensional figure composed of three sides and whose interior angles sum up to 180°. A triangle in spherical geometry, on the other hand, is a triangle formed by three arcs. Thus, it is three-dimensional, and the interior angles sum up to more than 180°. The difference is shown in the attached picture.