pythagorean theorem proof unit 4 project grace olson
TRANSCRIPT
![Page 1: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/1.jpg)
Pythagorean Theorem Proof
Unit 4 ProjectGrace Olson
![Page 2: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/2.jpg)
Four equal Right Triangles
a
aa
a
b
bb
b
cc
cc
![Page 3: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/3.jpg)
Find the area of the Large Square
a
b
a
b c
a
b
c
a
bcc
Find the area of the large square:
The area of a square = a side squared
The side is = a + b
The are of the square = (a + b)
= (a + b)(a + b)
= a + 2ab + b
2
22
![Page 4: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/4.jpg)
Find the area of a Triangle
a
b
a
b c
a
b
c
a
bcc
The area of the Triangles = ½ ab
![Page 5: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/5.jpg)
Find the area of Four Triangles
a
b
a
b c
a
b
c
a
bcc
The area of the four triangles =
4(½ ab) = 2ab1 2
3 4
![Page 6: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/6.jpg)
Find the area of the Small Square
a
b
a
b c
a
b
c
a
bcc
The area of the Small Square = c 2
![Page 7: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/7.jpg)
Restate the area of the Large Square
a
b
a
b c
a
b
c
a
bcc
The area of the Large Square = the area of the Small Square + the area of the Four Triangles
The area of the Small Square = c
+
The area of the Four Triangles =
4(½ ab) = 2ab
c + 2ab
2
1 2
3 4
2
2
![Page 8: Pythagorean Theorem Proof Unit 4 Project Grace Olson](https://reader036.vdocument.in/reader036/viewer/2022083005/56649f1e5503460f94c36023/html5/thumbnails/8.jpg)
Set the areas equal
a
b
a
b c
a
b
c
a
bcc
c + 2ab = a + 2ab + b Simplify
c + 2ab = a + 2ab + b
c = a + b
1 2
3 4
22
22 2
2
2 22