Teacher resources and professional development across the curriculum

Teacher professional development and classroom resources across the curriculum

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

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

 Behold!

 Think about the first picture as two squares together. What are the new side lengths of the two squares?   Close Tip Think about the first picture as two squares together. What are the new side lengths of the two squares?

 Problem B4 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?

 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 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?

 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
 Session 6: Index | Notes | Solutions | Video

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