Transcript 8.1 Similarity in Right Triangles


Remember that the highlighted terms are
called the means
a y

x b

If a, b, and x are positive and you have the
proportion
a x

x b

Then “x” is called the geometric mean
between “a” and “b”.

If the altitude is drawn to the hypotenuse of a right
triangle, then the two triangles formed are similar to
the original triangle and each other.
D
C
A
D
A
B
B
D
B
A
C
D
C
D
C
B
A
A
D
D
B
C
C
A
D
B
ABD
DBC
ADC

When the altitude is drawn to the hypotenuse of a
right triangle, the length of the altitude is the
geometric mean between the segments of the
hypotenuse.
D
A
B

C

D
A
B
C
Important reminder  hypotenuse will always be the numerator in the 1st ratio.
Leg CD

Leg AD
When the altitude is drawn to the hypotenuse of a right
triangle, each leg is the geometric mean between the
hypotenuse and the segment of the hypotenuse that is
adjacent (touching) to that leg.
R
C

When altitude is the
geometric mean.
X
S

When LEG RS is the
geometric mean.

When LEG CR is the
geometric mean.
K
Q
M

N


USING THE PREVIOUS
COROLLARY
Homework, pg. 288
CE 16,17
WE 22-26, 31-36