squared & square root if you are given the area of a square, the length of 1 side is the square...
TRANSCRIPT
Squared & Square Root
• If you are given the area of a square, the length of 1 side is the square root of that area!
• If you are given the length of one side, the area is that number squared!
17 units squared
???
√17
√8 ???
8 units sq.
√8 x √8 = 8
Baseball Field:What is the distance
from 2nd Base to home plate?From Pedroia to Varitek
90 ft.
90 ft.
90 ft.
90 ft.
Pythagorean Theorem (Theorem 65)
• In any right triangle, the sum of the squares of the legs equals the square of the hypotenuse.
leg2 + leg2 = hypotenuse2
or
a2+b2=c2
Pythagorean Theorem
a
b
c hypotenuse
Right Triangle
altitude(leg)
base(leg)
Pythagorean Theorem
Square
A = s2s
s
s
s
a
b
cA = a2
A = c2
A = b2
Pythagorean TheoremGeometric
Demonstration
a
b
c
Pythagorean TheoremGeometric
Demonstration
a
b
c
Pythagorean TheoremGeometric
Demonstration
a
b
c
Pythagorean TheoremGeometric
Demonstration
a
b
c
Pythagorean TheoremGeometric
Demonstration
Pythagorean Theorem
b
a2 + b2
=
c2
ac
If a2 + b2 = c2
Solve for c:a=4b=3c=?
Then:c2 = a2+ b2
c2= 42 + 32
c2= 16 + 9 c2=25√c2= √ 25c= 5
Summarizer:If a2 + b2 = c2
Solve for c when:a=6b=8c=?
Solve for c when:a=5b=12c=13
• How would you find the value of b, if you knew the values of a and c?
• How would you find the value of a, if you knew the values of b and c?
• How would you find the value of c, if you knew the values of a and b?
a2 + b2 = c2
How would you find the length of a leg?
a = √c2- b2
b = √c2- a2
c = √a2+ b2
Let’s Solve!What is the distance
from 2nd Base to home plate?(From Pedroia to Varitek)
90 ft.
90 ft.
90 ft.
90 ft.
