Altitude on Hypotenuse Theorems 9'3

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Altitude on Hypotenuse Theorems9.3
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Homework

• Sec Page Problems

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Right Triangles
Mountain Problems
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Right Triangles
Acute ?
Leg
Hypotenuse
Acute ?
Leg
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Right Triangles
? Isosceles right ?legs
?Scalene right no ?legs
?Scalene right no ?legs
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Right Triangles
Altitude from a vertex - to the line of the
opposite side
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Right Triangles
Altitude from a vertex - to the line of the
opposite side
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Right Triangles
Altitude from a vertex - to the line of the
opposite side
90
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Right Triangles
B
c
a
A
C
b
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Theorem

• Theorem The altitude drawn to the hypotenuse of
  a right triangle separates the triangle into two
  right triangles that are similar to each other
  and to the original triangle.

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Similarity
?ADC?ACB, ?CDB?ACB, ?ADC?CDB
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Similarity
?ADC?ACB, ?CDB?ACB, ?ADC?CDB
?D? ?C90 ?A? ?DCB ?B? ?DCA
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Theorem

• Theorem The length of the altitude to the
  hypotenuse of a right triangle is the geometric
  mean of the lengths of the segments of the
  hypotenuse.

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?ADC?ACB?CDB
C
A
B
D
CD2DADB
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Down2HideHide somewhere else
C
A
B
D
CD2DADB
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Theorem

• Theorem The length of each leg of a right
  triangle is the geometric mean of the length of
  the hypotenuse and the length of the segment of
  the hypotenuse adjacent to that leg.

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Down2HideHide somewhere else
C
A
B
D
AC2ABAD
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Theorem

• Theorem The length of each leg of a right
  triangle is the geometric mean of the length of
  the hypotenuse and the length of the segment of
  the hypotenuse adjacent to that leg.

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Down2HideHide somewhere else
C
A
B
D
CB2BDBA
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Theorem

• Theorem In a right triangle the product of the
  legs is equal to the product of the hypotenuse
  and the altitude to the hypotenuse.

ACCBABCD
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Theorem
C
A
B
D
ACCBABCD
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Mountain Problems
x
y
h
a
b
cab
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Mountain Problemsh2ab
h2ab
x
y
h
a
b
cab
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Mountain Problems
x2ac
x
y
h
a
b
cab
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Mountain Problems
y2bc
x
y
h
a
b
cab
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Problems

• 1.9.1
• ?ADC ? ?

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Problems

• 2. 9.1

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Problems

• 3. 9.1

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Problems

• 4. 9.1

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Problems

• 5. 9.1
• If AB2 and CB6,
• then BD?

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Problems

• Find
• x2
• y v(27)3v(3)
• z v(108) v(36)(3)6 v(3)

z
x4
y
3
9
(x4)2 (3)(39) x28x1636
x28x16-3636-36 x28x-200 (x10(x-2)0
x -10, 2
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Problems

• Find
• x 5
• y v(345)3v(15)
• z v(4548) 12v(15)

z
x7
y
3
48
(x7)2 (3)(48) x214x49144
x214x49-144144-144 x214x-950
(x19(x-5)0 x -19, 5
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x
y
h
a
b
cab
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