Problem 88. Triangle and Quadrilateral Areas, Midpoints
Level: High School, College, SAT Prep.

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: .

 

FACTS AND HINTS:

Geometry problem solving is one of the most challenging skills for students to learn. When a problem requires auxiliary construction, the difficulty of the problem increases drastically, perhaps because deciding which construction to make is an ill-structured 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. See Proposed Problem 87

---

3. AREA OF A TRIANGLE:

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