The Trisection of a arbitrary triangle. The trisection of a triangle can be achieved in several ways.
Presented here are four different problems detailing the trisection of an arbitrary triangle.

The first problem presented here is thus; If a triangle ABC is given and a random point P
on the one of the sides of the triangle is selected, construct two lines through P that trisects
the triangle into three regions of equal area.

Since P has the ability to be placed anywhere on one of the sides of the triangle then it is perhaps best to view this as a GSP animation. So click here for that animation.

The next problem presented is thus; Given a triangle ABC, find a point D such that line segments AD, BD, and CD trisect the area of the triangle into three regions with equal areas. Define D and prove that the triangle is divided into three regions of equal area. Show a construction for finding D.

The point D that we see is the intersection of the three medians of triangle ABC. That intersection point that we call the centriod of a triangle which is the balance point of the triangle.