In the figure below, given a
triangle AED, M and N are the midpoints of cevians AC and DB
respectively. If S1 and S2 are the areas of the quadrilaterals
AECN and DEBM 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. See Proposed Problem
87
3. AREA OF A TRIANGLE:
Median Area Fact:
A median divides the triangle into
two triangles of equal area.
