Download 4.7 – Square Roots and The Pythagorean Theorem

4.7 – Square Roots and The
Pythagorean Theorem
SQUARES and SQUARE ROOTS:
Consider the area of a 3'x3' square:
ft 2
32 = 9___
A = ____
3  3 = __
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
3
9 = ___
1
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)
170
3)
40
4)
125
2.5
13.1
6.5
11.3
2.24
13.01
6.32
11.18
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
2
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 2  b2  c2
c
a
b
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.
3
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
a=
5
b =12
subs:
52
+ 12 = 13
results:
25
+ 144 =
2
169
c = 13
=
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:
12
+ 1.5 =
1
+ 2.25 =
2
3.25
22
=
4
4
YES or NO
4
Homework : p. 253 # 6-48 EVEN
5