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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:
 .
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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.
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