Pythagorean Theorem

A WebQuest for 9th Grade Geometry

Designed by

Frank J. Tozlu
ftozlu@ycp.edu



 

Introduction | Task | Process | Evaluation | Conclusion 


Introduction

Pythagorean's Theorem has been solved several hundred different ways.  Pythagoras, for whom the famous theorem is named, lived during the 6th century B.C. on the island of Samos in the Aegean Sea, in Egypt, in Babylon and in southern Italy. Pythagoras was a teacher, a philosopher, a mystic and, to his followers, almost a god. His thinking about mathematics and life was riddled with numerology.

The Pythagorean Theorem exhibits a fundamental truth about the way some pieces of the world fit together. Many mathematicians think that the Pythagorean Theorem is the most important result in all of elementary mathematics. It was the motivation for a wealth of advanced mathematics, such as Fermat's Last Theorem and the theory of Hilbert space. The Pythagorean Theorem asserts that for a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides:

a2 + b2 = c2



It is also in this section that you'll communicate the Big Question (Essential Question, Guiding Question) that the whole WebQuest is centered around.
 
 



The Task

Obtain the Pythagorean Theorem as discovered by President J.A. Garfield in 1876.

You will be given the essential elements in which Garfield used to prove this theorem.  Check out the web links below to search for critical clues to obtain the solution.




The Process

1.   Find the formula for the area of a Trapizoid!

2.  Find the formula for the area of a Triangle!

Trapezoid
Triangle

The trapezoid will be constructed from two equal triangles with legs a and b.
Hint:  Set up one of triangles so that the small leg a is the top base of the trapizoid, and the other triangle with leg b as the bottom base of the trapiziod. (The height h of the left side of the trapiziod will then become a+b)

These two triangle together will form your trapiziod by connecting a line between the bases of the formed trapiziod made by the triangles.

Your figure should look something like this:




Set the area of the trapiziod equal to the sum of the areas of the three figures contained in your constructed trapezoid as shown above. 

Solve this equation, President Garfield did, to obtain the Pythagorean Theorem:

a2 + b2 = c2

Please show your all your work on a document to be handed in upon completion of the solution.




Evaluation

Performance will be evaluated in accordance the following scale. All grades are given as a group.


Beginning

1

Developing

2

Accomplished

3

Exemplary

4

Score

Completed drawing of individual parts of Trapiziod

 





 


Labeled all
parts of the final constructed figure with the appropriate area formula 



 





 

Established the equation for the interior parts of the constructed trapezoid.



 





 

Obtained the famous Pythagorean Theorem for the equations found in the figure.

 





 




Conclusion

Put a couple of sentences here that summarize what they will have accomplished or learned by completing this activity or lesson. You might also include some rhetorical questions or additional links to encourage them to extend their thinking into other content beyond this lesson.




Last updated on August 15, 1999. Based on a template from The WebQuest Page