4. 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

7. 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

8. The Pythagorean Theorem
Find the length of the hypotenuse:
8"
6"
x"

9. The Pythagorean Theorem
Proof of the Pythagorean Theorem:

10. The Pythagorean Theorem

11. The Pythagorean Theorem

12. The Pythagorean Theorem

13. The Pythagorean Theorem
A 35" T.V. has a height of
21". What is the width of
the screen?
21"
x"
The size of a television is measured by the length
of the screen’s diagonal.
a2
+ b2
= c2
x2
+ 441 = 1225
x2
= 784
x = 28

14. The Pythagorean Theorem
What is the distance from the free throw line to the back rim?
(Round to the nearest foot.)

15. 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

16. 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
+ 142
484 = 81 + 196 ?

17. Class Work: