Problem 87. Area
of Quadrilateral and Midpoints of Diagonals.
Level: High School, SAT Prep, College
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Quadrilateral and Midpoints of Diagonals, Math Education, High School,
College, Online Learning.
In the figure below, given a
quadrilateral ABCD, M and N are the midpoints of AC and BD
respectively. If S, S1, S2, and S3
are the areas of the quadrilaterals ABCD,BCNA, BCDM, and BCNM
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. AREA OF A TRIANGLE:
Median Area Fact:
A median divides the triangle into
two triangles of equal area.
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