Online Geometry Problems

Geometry Problem 89. Area of Triangle and Quadrilateral, Midpoints of Diagonals, Median of a triangle. High School, College, Math Education

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, prove that: Equal triangle area conclusion.

Problem about triangle area and midpoints




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).


Median Area Fact: A median divides the triangle into two triangles of equal area.

Median Area Fact 

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.

Mid Segment or Midline theorem



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