9.3 Altitude-On-Hypotenuse Theorems

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9.3 Altitude-On-Hypotenuse Theorems

• Objective
• After studying this section, you will be able to
  identify the relationships between the parts of a
  right triangle when an altitude is drawn to the
  hypotenuse

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When altitude CD is drawn to the hypotenuse of
triangle ABC, three similar triangles are formed.
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C
A
D
B
Therefore, CB is the mean proportional between AB
and DB
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Theorem If an altitude is drawn to the
hypotenuse of a right triangle, then a.
The two triangles formed are similar to the
given right triangle and to each other. b.
The altitude to the hypotenuse is the mean
proportional between the segments of the
hypotenuse.
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c. Either leg of the given right triangle
is the mean proportional between the
hypotenuse of the given right triangle and the
segment of the hypotenuse adjacent to that
leg (i.e. the projection of that leg on the
hypotenuse)
C
b
a
h
A
B
D
y
x
c
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Example 1
If AD 3 and DB 9, find CD
Example 2
If AD 3 and DB 9, find AC
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Example 3
If DB 21 and AC 10, find AD
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P
O
Given
R
K
J
M
Prove (PO)(PM) (PR)(PJ)
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Summary Summarize what you learned from todays
lesson.
Homework Worksheet 9.3