Alright, so we are given a triangle where all the angles are the same. Now - we need to write a proof that when IE bisects KM, it creates equal angles.
Given:
IKM is equiangular
IE is perpendicular to KM
This is enough to prove that IKE is congruent to IME because:
IEK and IEM are both 90 degrees, since IE is perpendicular to KM
KIE and MIE are the same degree measure, since I is being bisected.
This leaves us with only one angle remaining, and since we already know that the first two angles are congruent to their counterpart - we also know that IKE is congruent to IME because all interior angles of triangles add up to 180°, and we know the other two angle sets to be congruent.
