Introduction Introduction to the to the

Pythagorean Pythagorean TheoremTheorem

HOW IS THE PYTHAGOREAN THEOREM HOW IS THE PYTHAGOREAN THEOREM USED IN EVERYDAY LIFE?USED IN EVERYDAY LIFE?

The access ramp The access ramp will be covered with will be covered with an all-weather an all-weather carpet. Would you carpet. Would you be able to find the be able to find the area of the carpet area of the carpet needed?needed?

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What Is The Pythagorean Theorem?What Is The Pythagorean Theorem?

• The Pythagorean Theorem isThe Pythagorean Theorem is

AA2 2 + B2 = C2

• It is used when you are finding the missing sides of a right triangle.

Who Came Up With This Theorem?Who Came Up With This Theorem?

Pythagoras was a Pythagoras was a teacher and a teacher and a philosopher philosopher

Pythagoras lived during Pythagoras lived during the 6th century B.C. on the 6th century B.C. on the island of Samos the island of Samos

What Does The Theorem Mean?What Does The Theorem Mean?

Pythagoras found out that for a Pythagoras found out that for a right triangle the square of the right triangle the square of the hypotenuse is equal to the sum hypotenuse is equal to the sum of the squares of the other two of the squares of the other two sides:sides:

a and b are the legs, while c is a and b are the legs, while c is

the hypotenuse. The the hypotenuse. The hypotenuse is located opposite hypotenuse is located opposite the right angle and will be the the right angle and will be the longest side.longest side.

In Other WordsIn Other Words

The green square's The green square's area (with area Carea (with area C22) ) equals the sum of equals the sum of two others. two others. It is It is exactlyexactly the yellow the yellow square's area (Asquare's area (A22) ) plus the blue plus the blue square's (Bsquare's (B22).).

Pythagorean Theorem In Action!Pythagorean Theorem In Action!

Watch as this Watch as this animation animation demonstrates demonstrates what the what the theorem means.theorem means.

The area of the The area of the squares on the squares on the legs are brought legs are brought together to form together to form one square on one square on the hypotenuse.the hypotenuse.

Watch The Following Video ClipWatch The Following Video Clip

This will give This will give you a few you a few examples of examples of the the Pythagorean Pythagorean theorem in theorem in everyday life.everyday life.

Use the Pythagorean Theorem to Use the Pythagorean Theorem to solve this problem.solve this problem.

The shaded surface of The shaded surface of this access ramp will be this access ramp will be covered with all –covered with all –weather carpet. Find the weather carpet. Find the area of the carpet area of the carpet needed.needed.

Draw out the triangular Draw out the triangular prism on your paper and prism on your paper and solve.solve.

SolutionSolution

Was your answer one of the following?Was your answer one of the following?

A) 12 A) 12 B) 32 B) 32 C) 40 C) 40 D) 48 D) 48 E) 96E) 96

How to SolveHow to Solve

• First we needed to find the length of the First we needed to find the length of the hypotenuse. hypotenuse.

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AA2 2 + B+ B2 2 = C= C22

442 2 + 3 + 32 2 = C= C22

16 + 9 = C16 + 9 = C2 2

25 = C25 = C2 2

Find the square root of Find the square root of each side. each side.

C = 5C = 5

Find the Area of the shaded surface.Find the Area of the shaded surface.

To find the area of a To find the area of a rectangle take base rectangle take base times height.times height.

Our final answer will be Our final answer will be

40 units squared.40 units squared.

Therefore you would Therefore you would need 40 square feet of need 40 square feet of carpet to cover the ramp.carpet to cover the ramp. 88

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SummarySummary

Pythagorean Theorem is Pythagorean Theorem is AA22 + B + B22 = C = C22

Now you should have a good idea what the Now you should have a good idea what the Pythagorean Theorem is and how it works.Pythagorean Theorem is and how it works.

As you can see it is used in everyday life.As you can see it is used in everyday life.

We will be doing more work with it later on.We will be doing more work with it later on.