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.