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Session 6, Part B: Proving the Pythagorean Theorem
 
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Session 6, Part B:
Proving the Pythagorean Theorem

In This Part: What Is a Theorem? | Constructing a Proof | More Proofs

Below are two more proofs of the Pythagorean theorem, but only the pictures are given to you.

Problem B3

Solution  

This is a famous one-word proof written by the Hindu mathematician Bhaskara Acharya (1114-1185). What is the reasoning behind his proof?

Behold!

Stop! Do the above problem before you proceed. Use the tip text to help you solve the problem if you get stuck.
Think about the first picture as two squares together. What are the new side lengths of the two squares?   Close Tip

 

Problem B4

Solution  

James Garfield (1831-1881) was the 20th president of the United States. Five years before becoming president, he discovered this proof of the Pythagorean theorem. What is the reasoning behind his proof?

Stop! Do the above problem before you proceed. Use the tip text to help you solve the problem if you get stuck.
Compute the area of the figure two ways -- first by finding and adding the area of the three triangles and second by using the formula for the area of a trapezoid (1/2 • (sum of bases • height)). What must be true of the two areas you computed?   Close Tip

 

Problems B3 and B4 adapted from Connected Geometry, developed by Educational Development Center, Inc. pp. 198, 202. © 2000 Glencoe/McGraw-Hill. Used with permission. www.glencoe.com/sec/math

Next > Part C: Applications of the Pythagorean Theorem

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