TODAY F I N A L E X A M R E V I E W

R E V I E W F O R T E S T T O M O R R O W

R E V I E W F O R T E S T F R I D A Y

P Y T H A G O R E A N T H E O R E M

C L A SS W O R K

0)105()23( xx

)105()23( xx

22)105()23( xx

10523 xx

1022 x

x212

Isolate the radicals

Square both sides

Simplify

Subtract 3x from both sides

Add 10 to both sides

If there are two radicals, isolate both radicals by moving one to the other side of the equal sign.

x = 6

THE PYTHAGOREAN

THEOREM

Pythagorus

• Lived in southern Italy from 579 BC-475 BC

• Considered the first true mathematician

• Used mathematics as a means to understand the natural world

• First to teach that the earth was a sphere that revolves around the sun

The Pythagorean Theorem

Find the length of the hypotenuse:

8"

6"

x"

The Pythagorean Theorem

Proof of the Pythagorean Theorem:

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

The Pythagorean Theorem

A 35" T.V. has a height of 21". What is the width of the screen?

35"21"

x"

The size of a television is measured by the length of the screen’s diagonal.

a2 + b2 = c2

x2 + 441 = 1225x2 = 784

x = 28

The Pythagorean Theorem

What is the distance from the free throw line to the back rim?(Round to the nearest

foot.)

The Pythagorean Theorem

How far is the catcher's throw from home to 2nd base? Round to the nearest hundredth.

• Solution: x2 = 902 + 902 = 16,200 x = 127.28 ft

Identify a Right Triangle

Determine whether a triangle with lengths 9 inches, 14 inches, and 22 inches is a right triangle.

c2 = a2 + b2

222 = 92 + 142484 = 81 +

196 ?

Class Work: