The author presents a detailed analysis of the series of triangles that complement the angles of basic and special right triangles. The series of fractal triangles as identified in this book have gone unstudied until now. Every student of geometry must necessarily be aware of the existence of these distinct series of fractal triangles and understand their relationship to the basic and special right triangles. A must read for geometry and math students. The author foresees applications for these distinct series of fractal triangles in the field of nanotechnology and nano-triangles.