squared & square root if you are given the area of a square, the length of 1 side is the square...

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.