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Explorations of a Problem with Two Squares

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Visit this site: http://jwilson.coe.uga.edu/squareF/square.html

Author:Jim Wilson; Dept. of Mathematics Education, Univ. of Georgia
Description: Given a square of side s and segments drawn from each vertex to the midpoint of the second side, counting counter-clockwise, the segments intersect to form a new square. What is the ratio of the area of the shaded square to the area of the original square? Perhaps this is a "teachable moment" to discuss that in fact the shaded figure is a square. Why are the segments parallel and mutually perpendicular?

Levels: High School (9-12)
Languages: English
Resource Types: Lesson Plans and Activities, Documents/Sketches/Galleries, Geometer's Sketchpad
Math Topics: Graphing Equations, Constructions, Triangles and Other Polygons

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