An isoscelizer of an (interior) angle A in a triangle Δ A B C is a line through points I_(A B) I_(A C) where I_(A B) lies on A B and I_(A C) on A C such that Δ A I_(A B) I_(A C) is an isosceles triangle. An isoscelizer is therefore a line perpendicular to an angle bisector, and if the angle is A, the line is known as an A-isoscelizer. There are obviously an infinite number of isoscelizers for any given angle. Isoscelizers were invented by P. Yff in 1963. Through any point P draw the line parallel to B C as well as the corresponding antiparallel. Then the A-isoscelizer through P bisects the angle formed by the parallel and the antiparallel. Another way of saying this is that an isoscelizer is a line which is both parallel and antiparallel to itself.

angle bisector | antiparallel | congruent isoscelizers point | equal parallelians point | isosceles triangle | Yff center of congruence | Yff central triangle