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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: