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Squaring with Squares


One of the proofs of the Pythagorean Theorem typically uses squares constructed on each side of a right triangle (see figure below). The area of the square constructed on the hypotenuse (green square) is equal to the sum of the areas of the squares constructed on each of the legs of the triangle (blue squares).



View a dynamic version of this construction in Geometer's Sketchpad or in a java template.

Instead of using squares, can we use equilateral triangles? How about regular hexagons? Would these figures (or any others) give the same results?

What is so special about squares? In other words, why are squares typically used in this proof?


 Related External Resources

Heron's Area of a Triangle
This site will take you through some historical explorations, some interactive activities, and some intriguing connections in mathematics.

Geoboards in the Classroom
This unit deals with the side lengths and area of two-dimensional geometric figures using the geoboard as a pedagogical device.

Dissecting the Pythagorean Theorem
This lesson is for students to develop an understanding of how and why the Pythagorean theorem works. Also, students will gain an understanding of applications of the theorem and relate it to real world situations.



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