Pythagorean Theorem
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Transcript of Pythagorean Theorem
![Page 1: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/1.jpg)
a
b
c
222 cba
![Page 2: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/2.jpg)
This is a right triangle:
![Page 3: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/3.jpg)
We call it a right triangle because it contains a right angle.
![Page 4: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/4.jpg)
The measure of a right angle is 90o
90o
![Page 5: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/5.jpg)
The little square
90o
in theangle tells you it is aright angle.
![Page 6: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/6.jpg)
About 2,500 years ago, a Greek mathematician named Pythagorus discovered a special relationship between the sides of right triangles.
![Page 7: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/7.jpg)
Pythagorus realized that if you have a right triangle,
3
4
5
![Page 8: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/8.jpg)
and you square the lengths of the two sides that make up the right angle,
24233
4
5
![Page 9: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/9.jpg)
and add them together,
3
4
5
2423 22 43
![Page 10: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/10.jpg)
22 43
you get the same number you would get by squaring the other side.
222 543 3
4
5
![Page 11: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/11.jpg)
Is that correct?
222 543 ?
25169 ?
![Page 12: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/12.jpg)
It is. And it is true for any right triangle.
8
6
10222 1086
1006436
![Page 13: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/13.jpg)
The two sides which come together in a right angle are called
![Page 14: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/14.jpg)
The two sides which come together in a right angle are called
![Page 15: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/15.jpg)
The two sides which come together in a right angle are called
![Page 16: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/16.jpg)
The lengths of the legs are usually called a and b.
a
b
![Page 17: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/17.jpg)
The side across from the right angle
a
b
is called the
![Page 18: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/18.jpg)
And the length of the hypotenuse
is usually labeled c.
a
b
c
![Page 19: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/19.jpg)
The relationship Pythagorus discovered is now called The Pythagorean Theorem:
a
b
c
![Page 20: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/20.jpg)
The Pythagorean Theorem says, given the right triangle with legs a and b and hypotenuse c,
a
b
c
![Page 21: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/21.jpg)
then
a
b
c
.222 cba
![Page 22: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/22.jpg)
You can use The Pythagorean Theorem to solve many kinds of problems.
Suppose you drive directly west for 48 miles,
48
![Page 23: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/23.jpg)
Then turn south and drive for 36 miles.
48
36
![Page 24: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/24.jpg)
How far are you from where you started?
48
36?
![Page 25: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/25.jpg)
482
Using The Pythagorean Theorem,
48
36c
362+ = c2
![Page 26: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/26.jpg)
Why? Can you see that we have a right triangle?
48
36c
482 362+ = c2
![Page 27: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/27.jpg)
Which side is the hypotenuse? Which sides are the legs?
48
36c
482 362+ = c2
![Page 28: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/28.jpg)
22 3648
Then all we need to do is calculate:
12962304
3600 2c
![Page 29: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/29.jpg)
And you end up 60 miles from where you started.
48
3660
So, since c2 is 3600, c is 60.So, since c2 is 3600, c is
![Page 30: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/30.jpg)
Find the length of a diagonal of the rectangle:
15"
8"?
![Page 31: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/31.jpg)
Find the length of a diagonal of the rectangle:
15"
8"?
b = 8
a = 15
c
![Page 32: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/32.jpg)
222 cba 222 815 c 264225 c 2892 c 17c
b = 8
a = 15
c
![Page 33: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/33.jpg)
Find the length of a diagonal of the rectangle:
15"
8"17
![Page 34: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/34.jpg)
Practice using The Pythagorean Theorem to solve these right triangles:
![Page 35: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/35.jpg)
5
12
c = 13
![Page 36: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/36.jpg)
10
b
26
![Page 37: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/37.jpg)
10
b
26
= 24
(a)
(c)
222 cba 222 2610 b
676100 2 b1006762 b
5762 b24b
![Page 38: Pythagorean Theorem](https://reader036.fdocuments.in/reader036/viewer/2022081716/54553252af795992438b6977/html5/thumbnails/38.jpg)
12
b
15
= 9