11.4 Pythagorean Theorem

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2

1Definitions

Pythagorean Theorem

Practice Problems

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Definition

Right Triangle Has 1 angle that is 90˚ Denoted as a small square in the corner

Hypotenuse Longest side Never touches the 90˚ angle

Leg Remaining 2 sides of the triangle Both are always touching the 90˚ angle Can be different lengths, but both are always

smaller than the hypotenuse

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Right Triangles

Hypotenuse

Leg

Leg

Right Angle

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Pythagorean Theorem

a2 + b2 = c2

b

a c where…

a and b are legs

c is the hypotenuse

Note: it does not matter which leg is called a and b

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Finding the Length of the Hypotenuse

Find the length of the hypotenuse of a right triangle if a=8 and b=15

222 cba

222 158 c

222564 c

2289 c

2289 c

17c

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Finding the Length of a Missing Side

25

a

10

222 cba 222 2510 a

6251002 a

5252 a

100 100

5252 a

525a 91.22

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Checking to See if a Triangle is a Right Triangle

Given the side lengths of 20, 21, 29; determine if the triangle is a right triangle

222 cba 222 292120

841441400

841841

Both sides are equal, so it is a right triangle

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More Checking to See if a Triangle is a Right Triangle

Given the side lengths of 8, 10, 12; determine if the triangle is a right triangle

222 cba 222 12108

14410064

144164

Both sides are not equal, so it is not a right triangle

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Practice Problems

Page 608Problems 13-28, 41, 42

Even due todayOdd due next class