Rate of Change and Slope. Warm Up Solve each proportion for x.
Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a...
Transcript of Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a...
![Page 1: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/1.jpg)
8.1 Geometric Mean.notebook January 22, 2014
"Do Now"
Solve each proportion.
Ms. Stalvey ran a 5K over the weekend through downtown
Greenville in 23:55!
![Page 2: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/2.jpg)
8.1 Geometric Mean.notebook January 22, 2014
Unit 9: Right Triangles and Trigonometry8.1 Geometric Mean Date
GeometricMean
The positive square root of the product between two numbers
The means are the same in a proportion
![Page 3: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/3.jpg)
8.1 Geometric Mean.notebook January 22, 2014
Try examples 13 on your practice sheet
![Page 4: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/4.jpg)
8.1 Geometric Mean.notebook January 22, 2014
1. Cut out ABC.
(Cut around the letters of the vertices.)
![Page 5: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/5.jpg)
8.1 Geometric Mean.notebook January 22, 2014
2. On the 2nd copy, outline the two inside triangles.
Use green for ACD and blue for CBD.
![Page 6: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/6.jpg)
8.1 Geometric Mean.notebook January 22, 2014
3. In pencil, write the letters of the vertices inside each triangle.
Also, draw the right angle symbol inside ACD.
A
C C
BDD
![Page 7: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/7.jpg)
8.1 Geometric Mean.notebook January 22, 2014
C
BD
A
C
D
4. Cut out ACD and CBD.
Write the letters of the vertices on the back of each triangle.
![Page 8: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/8.jpg)
8.1 Geometric Mean.notebook January 22, 2014
C B
D
A C
D
5. Orient the 3 triangles the same way.
What do you notice?
3 similar triangles are formed by the altitude DC in the overall triangle!
![Page 9: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/9.jpg)
8.1 Geometric Mean.notebook January 22, 2014
C B
D
A C
D
Similarity Statement
~ ~
![Page 10: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/10.jpg)
8.1 Geometric Mean.notebook January 22, 2014
Try examples 4 and 5 on your practice sheet
![Page 11: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/11.jpg)
8.1 Geometric Mean.notebook January 22, 2014
C B
D
A C
D
How could we figure out the length of DC?
![Page 12: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/12.jpg)
8.1 Geometric Mean.notebook January 22, 2014
Big Idea #1
The altitude is the geometric mean of the smaller lengths of the hypotenuse
C B
D
A C
D
x y
h
x hh y
If CD is the altitude (going from the right angle to the hypotenuse) of the overall triangle, then
![Page 13: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/13.jpg)
8.1 Geometric Mean.notebook January 22, 2014
Big Idea #2
The leg of the overall right triangle is the geometric mean between the overall hypotenuse and the portion of the hypotenuse adjacent to that leg.
C B
D
A C
D
x y
x y
If CD is the altitude (going from the right angle to the hypotenuse) of the overall triangle, then
c
b a
b a
![Page 14: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/14.jpg)
8.1 Geometric Mean.notebook January 22, 2014
Try examples 69 on your practice sheet
![Page 15: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/15.jpg)
8.1 Geometric Mean.notebook January 22, 2014
![Page 16: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/16.jpg)
8.1 Geometric Mean.notebook January 22, 2014
![Page 17: Do Now Solve each proportion. - · PDF file"Do Now" Solve each proportion. Ms. Stalvey ran a 5K over the weekend through downtown Greenville in 23:55! ... Try examples 13 on your](https://reader034.fdocuments.in/reader034/viewer/2022052608/5a9e07c07f8b9a420a8cac52/html5/thumbnails/17.jpg)
8.1 Geometric Mean.notebook January 22, 2014