Area

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Ratio Proportion 8.1
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• Define ratio, proportion, and scale factor.

• Solve proportions.

• Solve real world problems.

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A scale factor describes how much the figure is
enlarged or reduced. If the scale factor of a
dilation is greater than 1 (k gt 1), it is an
enlargement. If the scale factor is less than 1
(k lt 1), it is a reduction.
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Solve the proportion.
7(72) x(56)
504 56x
x 9
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Solve the proportion.
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Solve the proportion.
(z 4)2 5(20)
(z 4)2 100
(z 4) ?10
(z 4) 10 or (z 4) 10
z 14 or z 6
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Solve the proportion.
3(56) 8(x)
168 8x
x 21
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Solve the proportion.
2y(4y) 9(8)
8y2 72
y2 9
y ?3
y 3 or y 3
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Solve the proportion.
d(2) 3(6)
2d 18
d 9
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Solve the proportion.
(x 3)2 4(9)
(x 3)2 36
(x 3) ?6
(x 3) 6 or (x 3) 6
x 3 or x 9
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EXAMPLE 3
The measures of the angles in ?CDE are in the
ratio of 1 2 3. Find the measures of the
angles.
m?C 30?, m?D 60?, m?E 90?
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The ratio of the angle measures in ?ABC 156.
What is the measure of each angle?
m?A 15?, m?B 75?, m?C 90?
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Tyler wants to find the height of a telephone
pole. He measured the poles shadow and his own
shadow and then made a diagram. What is the
height h of the pole?
31740 92h
h 345 in.
h 28 ft. 9 in.
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Find the length of the model to the nearest tenth
of a centimeter.
5(6.3) x(1.8)
31.5 1.8x
17.5 x
The length of the model is 17.5 centimeters.
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A boxcar has the dimensions shown. A model of
the boxcar is 1.25 in. wide. Find the length of
the model to the nearest inch.
1.25(36.25) x(9)
45.3 9x
x ? 5 inches
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In the diagram, ABBC is 2 7 and AC 36. Find
AB and BC.
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The measures of the angles of ?ABC are in the
ratio given. Find the measures of the angles of
the triangle.
a. 3 5 10 b. 2 7 9 c. 11 12 13
m?A 20?, m?B 70?, m?C 90?
m?A 55?, m?B 60?, m?C 65?
m?A 30?, m?B 50?, m?C 100?
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Find the length of side BC.
25r 10 135
30q 45 240
25r 125
30q 195
r 5
q 6.5
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Solve for x.
c.
X ?7
b.
X 9
a.
X 3
f.
e.
d.
X 6
X 12
X 18
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Assignment
Ratio and Proportion