The Pythagorean Theorem Slideshow 37, Mathematics Mr. Richard Sasaki, Room 307

ObjectivesObjectives Understand the relationship of the areas of the squares about a right-angled triangle Understand the relationship of the areas of the squares about a right-angled triangle Understand and derive the Pythagorean Theorem Understand and derive the Pythagorean Theorem Be able to implement the theorem in simple cases Be able to implement the theorem in simple cases

The Right-Angled Triangle Let’s review some vocabulary. Hypotenuse Legs As you know, there is a relationship between the legs on a triangle and its hypotenuse. Before that, consider the diagram below. A B C Let A, B and C be the areas of the given squares. What is the relationship between their areas? A + B = C Let’s try and prove this! Good luck!

Proof – Part 1 A B C G F H I D E K L

Proof – Part 2 A B C G F H I D E K L For the same reasons, square AHIC has the same area as KCEL. Adding both results, we get the total area of squares BAGF and AHIC being the total area of rectangles BKLD and KCEL, which is equal to the area of square BCED.

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The Pythagorean Theorem The Pythagorean Theorem, has hundreds of proofs. My favourite proof is Garfield’s proof. Consider a trapezium ABCD with two right angles as shown. A B C D E

The Pythagorean Theorem You will have an opportunity to learn more proofs in the Winter Homework. You should know at least one. Pythagorean Theorem: We can use the theorem to find missing lengths. Example Note: No length can be negative!

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Surds and Pythagoras As you saw in the last question, remember to simplify surds when you can! Example If it confuses you, don’t write it (unless you are told to)! This doesn’t simplify.

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