In the figure below, given a triangle
AED, M and N are the midpoints of cevians AC and DB
respectively. If S1, S2, and S3
are the areas of the triangles EBM, ECN, and BEC respectively,
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. Mid-Segment 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 one-half the length of the third side.