9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle,...
-
Upload
todd-sparks -
Category
Documents
-
view
214 -
download
0
Transcript of 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle,...
![Page 1: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/1.jpg)
9.1 Similar Right Triangles
![Page 2: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/2.jpg)
Theorem
If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right triangle.
ACDCBD
ABCACD
ABCCBD
A
B
C
D
![Page 3: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/3.jpg)
Since this is true
We have proportions.
ACDCBD
ABCACD
ABCCBD
A
B
C
D
BDABBC
BDABBCBC
AB
BD
BC
2
DBADAC
DBADACAC
DB
AD
AC
2
![Page 4: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/4.jpg)
Since this is true
The legs of the right triangle are the Geometric mean to the part of the hypotenuse and the whole hypotenuse.
ACDCBD
ABCACD
ABCCBD
DBADAC
DBADACAC
DB
AD
AC
2
BDABBC
BDABBCBC
AB
BD
BC
2
![Page 5: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/5.jpg)
Find x and y
Set up the proportions
12 8
x y
![Page 6: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/6.jpg)
Find x and y
Set up the proportions
12 8
x yx
x 812
12
y
y 128
8
![Page 7: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/7.jpg)
Find x and y
Set up the proportions
12 8
x y
154240
2012
812
12
2
x
x
x
x
104160
208
128
8
2
y
y
y
y
![Page 8: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/8.jpg)
Since this is true
The altitude is also a Geometric mean.
ACDCBD
ABCACD
ABCCBD
DBADCD
DBADCDCD
DB
AD
CD
2
A
C
D
B
12
8
6496
812
CD
CD
![Page 9: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/9.jpg)
Recapping
The Altitude is the geometric mean of the parts of the hypotenuse
A leg of the Original Right Triangle is the geometric mean of part of the hypotenuse touching it and the whole hypotenuse.
![Page 10: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/10.jpg)
Find x, y and z
x yz
615
![Page 11: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/11.jpg)
Find x, y and z
x yz
615
48.9103
90615
2.11143
1266156
7.17353
31561515
z
y
x
![Page 12: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/12.jpg)
• Solve for x, y and z
20
18
x
y
z
20
18
18
20 x
![Page 13: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/13.jpg)
• Solve for x, y and z
20
18
x
y
z
2.49
38
1876
32418400
181820
20
18
18
20
2
x
x
x
x
x
![Page 14: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/14.jpg)
• Solve for x, y and z
20
18
y
z 2.4
y
y 2.418
2.4
![Page 15: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/15.jpg)
• Solve for x, y and z
20
18
y
z 2.4
6.92.222.4
2.222.4
2.418
2.4
2
y
y
y
y
![Page 16: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/16.jpg)
• Solve for x, y and z
20
18
y
z 2.4
7.82.418 z
![Page 17: 9.1 Similar Right Triangles. Theorem If an altitude is drawn to the hypotenuse of a Right triangle, then it makes similar triangles to the original Right.](https://reader036.fdocuments.in/reader036/viewer/2022082709/56649d975503460f94a8030d/html5/thumbnails/17.jpg)
Homework
Page 531 – 534
# 11 – 33,41,42