A quadrisection of a triangle consists of two perpendicular segments which divide it into 4 regions of equal area. The quadrisection problem for triangles is to find the quadrisections of any triangle. Jacob Bernoulli (1687) and Leonhard Euler (1779) Index Number E729 have published papers on the problem. The following animations provide some help with visualizing solutions to the problem for various arcs of triangles.

The arc of isoseles triangles from the equilateral triangle E to I2, the only isosceles triangle with only two quadrisections.

The arc of isosceless triangles from E to I1, the isosceles triangle with minimum vertex angle greater than 60 degrees having only 1 quadrisection.

The arc of scalene triangles having only 2 quadrisections from I2 to I1. These form the border between triangles with 1 quadrisection and triangles with 3 quadrisections.