Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.
-
Upload
muhammad-carvin -
Category
Documents
-
view
214 -
download
1
Transcript of Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.
![Page 1: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/1.jpg)
Similar Right Triangles
Geometry
Chapter 9
A BowerPoint Presentation
![Page 2: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/2.jpg)
Index card activity
Cut an index card diagonally.
Here is the shape you will have.
[You actually have TWO of these triangles. Save one of them for later!]
![Page 3: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/3.jpg)
Index card activity
Draw an altitude from the right angle to the hypotenuse (you don’t need to use a protractor)
![Page 4: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/4.jpg)
Index card activity
How many triangles do you see?
![Page 5: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/5.jpg)
Index card activity
Cut along the altitude to split the big triangle into two smaller right triangles.
![Page 6: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/6.jpg)
Index card activity
You now have three triangles (this is the time to use the other half of the index card, which is exactly like your original triangle).
What do you notice about these three triangles?
![Page 7: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/7.jpg)
Index card activity
You now have three triangles (this is the time to use the other half of the index card, which is exactly like your original triangle).
What do you notice about these three triangles?
They are all SIMILAR to each other!
![Page 8: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/8.jpg)
Parts of a right triangle
![Page 9: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/9.jpg)
Parts of a right triangle
Here is an altitude from the right angle to the hypotenuse.
![Page 10: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/10.jpg)
Parts of a right triangle
Here is an altitude from the right angle to the hypotenuse.
![Page 11: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/11.jpg)
Parts of a right triangle
For our proportions, alt = altitude
and hyp = all of the hypotenuse
![Page 12: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/12.jpg)
Parts of a right triangle
= part of the hypotenuse next to
= part of the hypotenuse next to
![Page 13: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/13.jpg)
Altitude proportion
![Page 14: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/14.jpg)
Leg 1 proportion
![Page 15: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/15.jpg)
Leg 2 proportion
![Page 16: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/16.jpg)
Summary of proportions
![Page 17: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/17.jpg)
Solve for x
Does solving for x involve an altitude?
![Page 18: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/18.jpg)
Solve for x
Yes – x is an altitude
![Page 19: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/19.jpg)
Solve for x
Yes – x is an altitude
![Page 20: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/20.jpg)
Solve for x
Yes – x is an altitude
![Page 21: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/21.jpg)
Solve for x
Yes – x is an altitude
![Page 22: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/22.jpg)
Solve for y
Does solving for y involve an altitude?
![Page 23: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/23.jpg)
Solve for y
No – y is
![Page 24: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/24.jpg)
Solve for y
y is
![Page 25: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/25.jpg)
Solve for y
y is
![Page 26: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/26.jpg)
Solve for y
y is
![Page 27: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/27.jpg)
Solve for z
Does solving for z involve an altitude?
![Page 28: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/28.jpg)
Solve for z
No – z is
![Page 29: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/29.jpg)
Solve for z
z is
![Page 30: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/30.jpg)
Solve for z
z is
![Page 31: Similar Right Triangles Geometry Chapter 9 A BowerPoint Presentation.](https://reader038.fdocuments.us/reader038/viewer/2022110303/55175b845503460e6e8b4814/html5/thumbnails/31.jpg)
Solve for z
z is