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Q&A #3824


Pythagorean Theorem

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From: Marielouise (for Teacher2Teacher Service)
Date: Apr 30, 2000 at 19:19:08
Subject: Re: Pythagorean Theorem

There is no best way to teach the Pythagorean Theorem.  The better way is so
that your students can understand it.  If you are in a middle school, have
the students draw on graph paper a right triangle with three units and four
units on the perpendicular sides.  Have them place a square of three units on
the side of three and a square of four units on the side of four.  If they
draw a square on the diagonal side they will not be able to count the squares
as the paper will not be "in agreement" with squares on that side.  However,
have the students take the total number of squares (9 + 16 = 25) that they
have and build a square on the diagonal side.  They will find that this
matches.  This is not a proof but it should convince the students that in
this right triangle the sum of the areas of the squares built upon the two
legs of the right triangle has the same area as the square built upon the
hypotenuse.

The origin of this relationship is said to have started in Egypt where every
year after the flooding of the Nile River, farmers had to survey their
holdings.  Rope-stretchers built 12 strips of ropes with knots at the 3 and 7
foot positions.  Stakes were placed at the 3 and 7 as well as the two ends
(which were joined together) to form a right angle.

Throughout the history of mathematics  many mathematicians and ordinary
people have looked for different proofs of this relationship among the three
sides of the right triangle.  Your students might research these.

You might also wish to look at the following:

http://mathforum.org/dr.math/faq/faq.pythagorean.html

Why is the PT so important?   There are many answers at different levels of
mathematics.  For you it might be because it is the foundation for the
distance formula in algebra.

 -Marielouise, for the Teacher2Teacher service

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