7.1 Ratio and Proportions

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7.1 Ratio and Proportions
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Ratio and Proportion

• _______________________________________
• ________________________________________
• _______________________________________
• Word form
• Colon form
• Fraction form
• _______________________________________

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• A poster is 3 feet long and 20 inches wide. Find
  the ratio of length to width.
• Comparing feet
• Comparing inches

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60
A
10
60
E
5x
30
B

1. Find the ratio of AE to BE.
2. Find the ratio of the largest angle of Triangle
   A to smallest angle of triangle B.

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3. A telephone pole 7 meters tall snaps into two
parts. The ratio of the two parts is 32. Find
the length of each part.
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A
B
6
C
D
10
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The measures of the angles of a triangle are in
the ratio of 345. Find the measures of each
angle.
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7.2 Properties of Proportions
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A proportion is a set of two equal
ratios _____________________________________
_____________________________________
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• The Means and Extremes Property
• _____________________________________
• ______________________________________
• ______________________________________

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Properties of Proportions
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(No Transcript)
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A
D
B
C
E

• If CE2, AB6 and AD3 then EB______
• 2. If AB10, DB8 and CB7.5 then EB______

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A
D
B
C
E

• BA12, BE10, EC5
• Find BD______ DA_____

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7.3 Similar Polygons
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• __________________________________________
• __________________________________________
• __________________________________________
• Two polygons are similar if their vertices can be
  paired so that
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• _________________________________________
• __________________________________________
• __________________________________________

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B
W
A
C
V
X
Y
Z
D
E
List congruent Angles
List Proportions of sides
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If polygons are similar then the ratio of the
lengths of two corresponding sides is called the
Scale Factor
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y
D
D
C
C
30
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x
z
A
B
50
A
B
30
a) Scale Factor
a) Find x, y, z
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The ratio of the perimeters of two similar
figures is equal to the Scale Factor.
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z
D
D
C
C
x
2.5
10
5
A
B
3
A
B
y
a) Scale Factor
a) Find x, y, z
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a) Scale Factor
b) Angle D____
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D
D
C
C
60
100
6
5
A
B
12
A
B
4
c) Find CB, AD, DC
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7.4 Proving Triangles areSimilar
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Postulate 15 ________________________ ___________
________________________ _________________________
__________
A
X
Y
B
C
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• When there are triangles within Trianlges
• _______________________________
• _______________________________

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Are the triangles similar? Find the scale
factor._______ Solve for x_______
3
5
1
x
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Find x______ and y______
Scale Factor____
x
8
3
y
3
4
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A
D
O
B
C
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7.5 More Similar Triangles
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Theorem 7.1 __________________________
______________________________________ __________
____________________________ _____________________
_________________
12
3
5
20
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Theorem 7.2 ___________________________ ________
_______________________________
12
28
3
7
5
20
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• How do we know what sides of the triangles to
  compare?
• _______________________________________
• ________________________________________
• __________________________________

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What reason are the Triangles ?
6
10
3
5
3
5
6
6
6
10
32
Def of ______________________________ ________
______________________________ ___________________
___________________ Means and Extremes Property
__________ _____________________________________
_____________________________________
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A
D
B C
E
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10
x
y
9
15
16
Solve for x and y Scale Factor?____
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7.6 Proportional Lengths
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Divide Proportionally means _____________________
___________________ ______________________________
__________
Triangle Proportionality Theorem ________________
__________________________________________________
__________________________________________
a
c
b
d
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Corollary ____________________________ __________
___________________________
a
c
b
d
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Triangle Angle Bisector _________________________
______________ ___________________________________
____ _______________________________________ _____
__________________________________
c
a
b
d
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Examples
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5x
10
5
40
x
10
12
24
41
x
4
2
x2