1.
6.2 Use Proportions to Solve Geometry Problems
6.2
Bell Thinger
Solve each proportion.
6
1. 3 =
8
x+1
ANSWER
15
8 = x+1
3
6
ANSWER 15
2.
3.
3 =
8
6
x+1
ANSWER
15
4. The area of a rectangle is 750
square meters. The ratio of the
width to the length is 5 : 6. Find
the width and the length.
ANSWER
width: 25 m; length: 30 m
3.
Example 1
6.2
In the diagram, MN = NP
RS
ST
Write four true proportions.
SOLUTION
Because MN = NP , then 8 = 4
RS
ST
x
10
By the Reciprocal Property, the reciprocals are
10
equal, so x
=
4
8
By Property 3, you can interchange the means, so
10
8
=
x
4
By Property 4, you can add the denominators to the
numerators, so
8 + 10
4 + x , or 18
=
=
10
x
10
4+x .
x
4.
Example 2
6.2
ALGEBRA In the diagram, BD = BE .
DA EC
Find BA and BD.
SOLUTION
BD
DA
BD + DA
DA
x
3
6x
=
=
=
=
BE
EC
BE + EC
EC
18 + 6
6
3(18 + 6)
x = 12
Given
Property of Proportions (Property 4)
Substitution Property of Equality
Cross Products Property
Solve for x.
So, BA = 12 and BD = 12 – 3 = 9.
6.
Example 3
6.2
Blueprints The blueprint shows a scale
drawing of a cell phone. The length of the
antenna on the blueprint is 5 centimeters. The
actual length of the antenna is 2 centimeters.
What is the scale of the blueprint?
SOLUTION
To find the scale, write the ratio of a length in the
drawing to an actual length, then rewrite the ratio so
that the denominator is 1.
length on blueprint
5÷2
5 cm
2.5
= 2 cm = 2 ÷ 2 =
1
length of antenna
The scale of the blueprint is 2.5 cm : 1 cm.
7.
Guided Practice
6.2
In the diagram, MN = NP
RS
ST
1. Find the value of x.
ANSWER
5
2. Suppose the length of the antenna on the blueprint
is 10 centimeters (actual length 2 cm). Find the
new scale of the blueprint.
ANSWER
5 cm
1 cm
8.
Example 4
6.2
Maps
The scale of the map at the right
is 1 inch : 26 miles. Find the actual
distance from Pocahontas to
Algona.
SOLUTION
Use a ruler. The distance from
Pocahontas to Algona on the map
is about 1.25 inches. Let x be the
actual distance in miles.
distance on map
1.25 in.
1 in.
=
x mi
actual distance
26 mi
x = 1.25 (26)
Cross Products Property
Simplify.
x = 32.5
The actual distance from Pocahontas to Algona is
about 32.5 miles.
9.
Example 5
6.2
Scale Model You buy a 3-D scale
model of the Reunion Tower in
Dallas, TX. The actual building is 560
feet tall. Your model is 10 inches
tall, and the diameter of the dome on
your scale model is about 2.1 inches.
a.
What is the diameter of the actual dome?
b. About how many times as tall as your model is the
actual building?
10.
Example 5
6.2
SOLUTION
a.
10 in. = 2.1 in.
560 ft
x ft
10 x = 1176
x = 117.6
measurement on model
measurement on actual building
Cross Products Property
Solve for x.
The diameter of the actual dome is about 118 feet.
b. To simplify a ratio with unlike units, multiply by a
conversion factor.
560 ft
10 in.
=
560 ft
10 in.
12 in.
= 672
1 ft
The actual building is 672 times as tall as the model.
11.
Guided Practice
6.2
4. Two cities are 96 miles from each other. The cities
are 4 inches apart on a map. Find the scale of the
map.
ANSWER
1 in : 24 mi
12.
Exit Slip
6.2
1. In the diagram, RS = ST . Write four true
XY
YZ
proportions.
ANSWER
45 = 30
30 = x
24
45
Sample answer :
= x ; 45
x ;
24 ; 24
30
45 + 30 = 24 + x
x
30
13.
Exit Slip
6.2
PS
2. In the diagram, MR =
. find MN and MR.
SN
RN
ANSWER
48; 30
14.
Exit Slip
6.2
3.
On a map, a street is 2 inches long. The actual
length is 1 mile. Find the scale.
ANSWER
4.
1 in. : 0.5 mi
A map’s scale is 1 cm : 20 km. If two towns are
8.2 centimeters apart on the map, what is the
actual distance between them?
ANSWER
164 km
15.
Exit Slip
6.2
5.
Solve
ANSWER
6.
1 = 3
s+8
36
4
Find the geometric mean of 42 and 12.
ANSWER
6 14
16.
Exit Slip
6.2
7.
The extended ratio of the angles of a triangle is
5: 12: 13. Find the angle measures of the triangle.
ANSWER
8.
30 , 72°, 78°
The area of a rectangle is 720 square inches. If the
ratio of the length to the width is 5 : 4, find the
perimeter of the rectangle.
ANSWER
108 in.
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