Pythagorean Theorem

Lesson Plan for grades 9-12

Erica Papa

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1. Title Page2. Table of contents3. Where did the Pythagorean Theorem come from? 4. Pythagoras5. Pythagorean Theorem equation6. Can you label the triangle?7. Leading to Pythagorean Triples8. Pythagorean Triples 9. Example 110. Example 211. To the Quiz12. Question #113. Question #214. Question #315. Question #416. Question #517. Find Homework Sheet

Where did this come from???

Over 2,500 years ago, a Greek mathematician named Pythagoras popularized the concept that a relationship exists between the hypotenuse and the legs of right triangles and that this relationship is true for all right triangles. 

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Pythagoras The Egyptians knew of this concept, as it related to 3, 4, 5

right triangles, long before the time of Pythagoras.  It was Pythagoras, however, who generalized the concept and who is attributed with its first geometrical demonstration.  Thus, it has become known as the Pythagorean Theorem.

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= the Pythagorean Theorem

"In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.“

This relationship can be stated as:

For any RIGHT TRIANGLE

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Can you label the triangle?

bc

aa, b are legs

c is the hypotenuse(c is across from the hypotenuse)

leg hypotenuse

leg

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There are certain sets of numbers that have a very special property in relation to the Pythagorean Theorem.  Not only do these numbers satisfy the Pythagorean Theorem, but any multiples of these numbers also satisfy the Pythagorean Theorem. 

WHAT IS IT? Click here

to find out!

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Pythagorean TriplesFor example:  the numbers 3, 4, and 5 satisfy the Pythagorean Theorem.  If you multiply all three numbers by 3  (9, 12, and 15), these new numbers ALSO satisfy the Pythagorean theorem!   5

3

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Example 1

A

BC

9m

12m

x

a

b

c

c2= a2+b2

x2= 81+144x2= 225

x=15

Answer: 15 m

=

Find x.

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Example 2

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A triangle has sides 6, 7 and 11.Is it a right triangle?

c2= a2+b2

112 ? 62+72

121? 36+49121≠ 85

Let a = 6, b = 7 and c = 11. The longest side MUST be thehypotenuse, so c = 11. Now, check to see if the PythagoreanTheorem is true.

Since the Pythagorean Theorem is NOT true, this triangle is NOT a right triangle.

Now it’s time to test your knowledge!

To the Quiz!

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Question #1

Find x

X= 15

X= 7

X= 26

X= 24

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Question #2

The lengths of the perpendicular sides of a right angled triangle 12 cm. and 16 cm. Then find the length of hypotenuse.

X

12 cm

16 cm

Find X

X= 144

X= 20

X= 192

X= 32

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Question #3To get from point A to point B you must avoid walking through a pond.  To avoid the pond, you must walk 34 meters south and 41 meters east.  To the nearest meter, how many meters would be saved if it were possible to walk through the pond? 

Choose:

22 meters

53 meters

75 meters

41 meters

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Question #4Oscar's dog house is shaped like a tent.  The slanted sides are both 5 feet long and the bottom of the house is 6 feet across.  What is the height of his dog house, in feet, at its tallest point?

Choose:

X= 3

X= 4

X= 4.5

X= 4

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Question #5

How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall?

Find X

X= 15.4 m

X= 14.5 m

X= 10.2 m

X= 4 m

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Sorry Try Again!

Back to Question #1 Back to Question #2 Back to Question #3 Back to Question #4 Back to Question #5

I finished the quiz!

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You’re correct!

Back to Question #1 Back to Question #2 Back to Question #3 Back to Question #4 Back to Question #5

I finished the quiz!

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I love the Pythagorean Theorem and I want to do more!

Click the right triangle to print off the page for your homework and hand it in tomorrow to be graded.

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Sorry, Try again

Back to find my homework!