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**Introduction to the Pythagorean Theorem**

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

The access ramp will be covered with an all-weather carpet. Would you be able to find the area of the carpet needed? 3 4

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**What Is The Pythagorean Theorem?**

The Pythagorean Theorem is A2 + B2 = C2 It is used when you are finding the missing sides of a right triangle.

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**Who Came Up With This Theorem?**

Pythagoras was a teacher and a philosopher Pythagoras lived during the 6th century B.C. on the island of Samos

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**What Does The Theorem Mean?**

Pythagoras found out that for a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides: a and b are the legs, while c is the hypotenuse. The hypotenuse is located opposite the right angle and will be the longest side.

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In Other Words The green square's area (with area C2) equals the sum of two others. It is exactly the yellow square's area (A2) plus the blue square's (B2).

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**Pythagorean Theorem In Action!**

Watch as this animation demonstrates what the theorem means. The area of the squares on the legs are brought together to form one square on the hypotenuse.

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**Watch The Following Video Clip**

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

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

The shaded surface of this access ramp will be covered with all –weather carpet. Find the area of the carpet needed. Draw out the triangular prism on your paper and solve.

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**Solution B) 32 C) 40 D) 48 E) 96 Was your answer one of the following?**

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**How to Solve 3 4 A2 + B2 = C2 42 + 32 = C2 16 + 9 = C2 25 = C2**

First we needed to find the length of the hypotenuse. A2 + B2 = C2 = C2 = C2 25 = C2 Find the square root of each side. C = 5 3 4

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

To find the area of a rectangle take base times height. Our final answer will be 40 units squared. Therefore you would need 40 square feet of carpet to cover the ramp. 5 8

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**Summary Pythagorean Theorem is A2 + B2 = C2**

Now you should have a good idea what the Pythagorean Theorem is and how it works. As you can see it is used in everyday life. We will be doing more work with it later on.

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EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.

EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.

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