Basically, Morley's Theorem gives the trisector of the angles in all three angles at any ∆ABC so that from the points of intersection, three points have obtained that form an equilateral triangle. But, if the angle trisector is given only at two angles, then an equilateral triangle cannot be formed, either using an inner angle trisector, an outer angle trisector, or a supplementary angle trisector. Based on these problems, it will be shown that by providing an inner angle trisector or an outer angle trisector at both non-right angles of any right triangle ABC an equilateral triangle can be formed. But by providing the supplementary angle trisector at a non- right angle, it will form a rhombus.

Keywords : Inner Angle Trisector, Outer Angle Trisector, Supplementary Angle Trisector, Morley’s Theorem.