9.3 Geo Bauer.notebook
January 28, 2015
(9.3) Altitude­on­Hypotenuse Theorems
right angle
C
When altitude CD is drawn to the hypotenuse AB, three similar triangles are formed.
altitude
C
A
B
D
hypotenuse
C
C
A
If one side of a triangle is a hypotenuse, then the opposite angle must be a right angle.
A
D
Jan 20­3:54 PM
C
long leg
Large
Hypotenuse
Large
A
B
D
C
C
Hypotenuse
Small
D
Setting up Proportions
short leg
Large
B
C
A
C
Setting up Proportions
D
B
D
Jan 20­4:02 PM
Hypotenuse
Large
A
B
A
B
C
short leg
Small
D
Hypotenuse
Medium
B
A
Jan 20­4:02 PM
long leg
Medium
B
Jan 20­4:02 PM
1
9.3 Geo Bauer.notebook
January 28, 2015
C
Setting up Proportions
Altitude­on­Hypotenuse Theorem
C
long leg
Small
short leg
Small
b
A
h
B
D
A
C
C
y
B
D D
long leg
Medium
B
Jan 20­4:02 PM
Altitude­on­Hypotenuse Theorem
C
b
h
A
a
c
short leg
Medium
A
D
x
If an altitude is drawn to the hypotenuse of a right triangle:
D
x
Jan 21­7:38 AM
the altitude to the hypotenuse is the mean proportional between the segments of the hypotenuse.
Altitude­on­Hypotenuse Theorem
C
b
h
a
y
A
B
c
Jan 21­7:38 AM
or
D
x
a
y
either leg of given Δ is the mean proportional between the hypotenuse of the given Δ and the segment of the hypotenuse adjacent to that leg.
B
c
or
Jan 21­7:38 AM
2
9.3 Geo Bauer.notebook
A
3
January 28, 2015
Practice Problems...
Practice Problems...
D
Solve for x.
D
9
X
18
A
Solve for x.
X
B
C
B
Jan 21­8:29 AM
10
C
Jan 21­8:29 AM
Practice Problems...
C
A
4
(9.3) Pg. 379: 1, 2, 5, 7, 11, 12, 16, 17, 21
Solve for x.
X
D
21
Jan 21­8:29 AM
B
Jan 21­9:08 AM
3