In the figure below, given a
triangle ABC, AD, BE, and CF are concurrent cevians at G. Prove
that:

FACTS AND HINTS:
Geometry theorem proving is one of the most challenging skills for students to learn. When a proof requires
auxiliary construction, the difficulty of the problem increases
drastically, perhaps because deciding which construction to make is an illstructured problem.
By “construction,” we mean adding geometric figures (points, lines, planes) to a problem figure that wasn’t mentioned as
"given."
1. CEVIAN:
A cevian is a line segment which joins a vertex of a triangle with a point on the opposite side (or its extension).
2. AREA OF A TRIANGLE:
Proposition:
The area of a triangle equals
onehalf the product of the length of a side and the length of
the altitude to that side.
