In the figure below, given a triangle
AED, M and N are the midpoints of cevians AC and DB
respectively. If S_{1}, S_{2}, and S_{3}
are the areas of the triangles EBM, ECN, and BEC respectively,
prove that:
.
HINTS:
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:
Median Area Fact:
A median divides the triangle into
two triangles of equal area.
3. MidSegment or Midline of a
Triangle Theorem: If a line MN joins the midpoints of two
sides of a triangle, then it is parallel to the third side and
its length is onehalf the length of the third side.
