Download 4.5 * Perimeter and Area

4.7 – Square Roots and The
Pythagorean Theorem
SQUARES and SQUARE
ROOTS:
Consider the area of a 3'x3' square:
A=3x3
A = (3)2 = 9
A = 3 or what POSITIVE number you can
multiply by itself to result in the answer of 9.
3 is called the SQUARE ROOT of 9
9 =3
Squares and Square Roots you should know:
x 1 2 3 4
x2 1 4 9 16
5
25
6 7 8 9 10 11 12 13 14 15
36 49 64 81 100 121 144 169 196 225
Estimate the square roots of the following numbers and then
use your calculator to compute the actual values:
1) 5
2)
 2.3
 13.1
 6.2
 11.2
2.236
13.038
6.325
11.180
170
3)
40
4)
125
THE PYTHAGOREAN
THEOREM:
Pythagoras was a Greek mathematician from
6th century BC. He discovered a unique
relationship between the sides of a right
triangle.
HYPOTENUSE
LEG
LEG
The sides adjoining the right angle are called
the LEGS of the triangle.
The side opposite the right angle is called the
HYPOTENUSE.
Pythagorean Right Triangle Theorem:
The sum of the squares of the legs of a right
triangle is equal to the SQUARE of the
hypotenuse.
In symbols: if a and b are the legs and c is the
hypotenuse of the right triangle then:
a b  c
2
2
c
a
b
2
Conversely:
If the square of the length of one side of a
triangle equals the SUM of the squares of the
other two sides then the triangle is
a RIGHT triangle.
Examples:
1.) If the sides of a triangle measure 5, 12, and 13
inches can it be a right triangle?
Pythagorean Formula:
a2 + b2 = c2
2
a= 5
subs:
5
b =12
results:
25
c = 13
2
+ 12 = 13
+ 144 =
169
=
2
169
169
YES or NO
Examples:
1.) Is the triangle that has sides that measure: 1,
1.5, and 2 yards a right triangle?
Pythagorean Formula:
a2 + b2 = c2
a=
1
b =1.5
c=
2
subs:
results:
2
2
+ 1.5
1
+ 2.25=
1
3.25
=
2
2
=
YES or NO
4
4
Homework :
Section 4.7
pages 253-255
#’s 6-48 EVEN