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 Discussion: All Topics Topic: Pythagorean Theorem Related Item: http://mathforum.org/mathtools/tool/1361/

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 Subject: Pythagorean Theorem Author: jon Date: Feb 15 2004
http://www.ies.co.jp/math/products/geo2/applets/pythasvn/pythasvn.html

This was a really cool Pythagorean Applet.  So many times, students can get away
without actually knowing some theory behind the formula they're using.  They can
see the variables in such an equation as the Pythagorean Theorem as universal
and unchanging (i.e. They may be confused when asked to find the length of the
third side of some triangle XYZ instead of ABC).

It seems that this applet has two uses.
1.) It helps students see that it doesn't matter how big or small the other two
squared sides will be, the sum of the two will alway equal that third side
squared.
2.) The squaring of the sides correlates to taking the area of a square whose
length is the side of one of the triangle's sides.  By repiecing the smaller
squares into the hypotenuses' square, the students really get to visually see
that the squares of the two sides equals the square of the hypotenuse.

Some drawbacks of this:

1.) Perhaps students will not see the connect between the areas of the squares
and the lengths of sides of the triangles.  (Although I thought that the diagram
at top was a pretty good explanation.)

2.) A small drawback of this is that the third side is fixed.  I guess it
doesn't really matter that much that you're not able to change the third side
too, but it'd be nice to have a fully movable triangle.
-However, this might be able to spark some discussion, as to why the third
side is constant or why you only have certain squares that fit this criterion.
It might help student see the relationship of the 2 sides to the hypotenuse.