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**Objective The student will be able to:**

use the Pythagorean Theorem

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**What is a right triangle?**

hypotenuse leg right angle leg It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are called legs. The side opposite the right angle is the hypotenuse.

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**The Pythagorean Theorem**

In a right triangle, if a and b are the measures of the legs and c is the hypotenuse, then a2 + b2 = c2. Note: The hypotenuse, c, is always the longest side.

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**Find the length of the hypotenuse if 1. a = 12 and b = 16.**

= c2 = c2 400 = c2 Take the square root of both sides. 20 = c

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**Find the length of the hypotenuse if 2. a = 5 and b = 7.**

= c2 = c2 74 = c2 Take the square root of both sides. 8.60 = c

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**Find the length of the hypotenuse given a = 6 and b = 12**

180 324 13.42 18

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**The Pythagorean Theorem**

7.3 – Square Roots and The Pythagorean Theorem Find the length of the hypotenuse of the given right triangle. The Pythagorean Theorem: hypotenuse 5 feet a c b 12 feet

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**The Pythagorean Theorem**

7.3 – Square Roots and The Pythagorean Theorem Find the length of the hypotenuse of the given right triangle. The Pythagorean Theorem: hypotenuse 4 feet a c b 7 feet Use the Square Root Table

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**What are Pythagorean Triples?**

Three integers that make the equation a2 + b2 = c2 true are called Pythagorean Triples. The numbers 3, 4 and 5 are a very famous Pythagorean Triple. a2 + b2 = c2 = 52 = 25

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