Transcript CHAPTER 11 NOTES - Dripping Springs Independent School

Chapter 11 Notes
Irrationals and the
Pythagorean Theorem
11-1 Square Roots and
Irrational Numbers
1
12 = 1
2
22 = 4
3
32 = 9
Squares have congruent sides so the area of a square is
the side length times itself. This is called squaring the side
length. The square of an integer is a perfect square.
The inverse of squaring a number is finding the square
root.
11-1 Square Roots and Irrational
Numbers
11-1 Square Roots and Irrational
Numbers-answers
5
4
7
3
8
10
7
9
6
12
5
13
-10
4/9
2/5
30
.4
11/12
An irrational number has a decimal form that neither
terminates nor repeats. IT CANNOT BE WRITTEN AS
THE RATIO OF TWO INTEGERS.
EXAMPLES OF IRRATIONAL NUMBERS:
.120120012….. - never repeats or terminates
π - never repeats or terminates
Square root of 18 - 18 is not a perfect square
EXAMPLES OF RATIONAL NUMBERS (CAN BE MADE
INTO A RATIO) -
432.8 - terminating decimal 432 4/5
.1212 - repeating decimal
12/99
11-1 Square Roots and Irrational
Numbers
11-1 Square Roots and Irrational
Numbers-answers
rational
rational
irrational
rational
irrational
7,-7
4,-4
About 4 mi
irrational
18 mi
About 25 mi
11-2 Pythagorean Theorem
HYPOTENUSE- always the longest
side and across from the right angle
c
a
LEGS
b
Formula:
a2 + b2 = c2
(Must always be a right triangle)
11-2 Pythagorean Theorem
a2 +b2 = c2
Use table on page 800
11-2 Pythagorean Theorem
a2 +b2 = c2
answers
52 + 6 2 = c 2
25 + 36 = c2
56 = c2
C = √56
C≈7.45
42 +72 =c2
16 + 49=c2
65 = c2
C=√65
C≈8.06
62 +82 =c2
36 + 64 = c2
100 = c2
C = √100
C = 10
11-2 Pythagorean Theorem
11-2 Pythagorean Theorem
answers
a 2 + 42 = 72
a2 + 16 = 49
a2 = 49-16
a2 = 33
a = √33
a ≈ 5.74
a2 + 102 = 122
a2 + 100 = 144
a2 = 144-100
a2 = 44
a = √44
a ≈ 6.63
a2 + 142 = 152
a2 + 196 = 225
a2 = 225-196
a2 = 29
a = √29
a ≈ 5.39
11-2 Pythagorean Theorem
Application
Now you can use a calculator but you must show work!
11-2 Pythagorean Theorem
Answer
The pond is 65
yards long.
162 +632 =c2
256 + 3969=c2
4225 = c2
C=√4225
C= 65
11-2 Pythagorean Theorem
Application
11-2 Pythagorean Theorem
Answer
11.5
a2 + 62 = 132
a2 + 36 = 169
a2 = 169-36
a2 = 133
a = √133
a ≈ 11.5
11-2 Pythagorean Theorem
Application
11-2 Pythagorean Theorem
Answer
30
a2 + 162 = 342
a2 + 256 = 1156
a2 = 1156-256
a2 = 900
a = √900
a = 30
11-2 Pythagorean Theorem
11-2 Pythagorean Theorem
Answers
10
62 +82 =c2
36+ 64=c2
100 = c2
C=√100
C= 10
11-2 Pythagorean Theorem
Pythagorean Triples - saves you time when working with
right triangles
3,4,5 or 5,12,13
You can also have their multiplies: 6,8,10 or 9,12,15 by
using scale factor.
Refer to the class notes handout
on Pythagorean Triples!