Name LESSON
7-5
Date
Class
Practice B Using Proportional Relationships
Refer to the figure for Exercises 1–3. A city is planning an outdoor concert for an Independence Day celebration. To hold speakers and lights, a crew of technicians sets up a scaffold with two platforms by the stage. The first platform is 8 feet 2 inches off the ground. The second platform is 7 feet 6 inches above the first platform. The shadow of the first platform stretches 6 feet 3 inches across the ground. 1. Explain why ABC is similar to ADE. (Hint: The sun’s rays are parallel.)
% 7 ft 6 in.
#
8 ft 2 in.
$
! 6 ft 3 in. " _ _
Possible answer: Because the sun’s rays are parallel, BC DE. ABC and ADE are congruent corresponding angles, and A is common to both triangles. So ABC ADE by AA . 2. Find the length of the shadow of the second platform in feet and inches to the nearest inch. 3. A 5-foot-8-inch-tall technician is standing on top of the second platform. Find the length of the shadow the scaffold and the technician cast in feet and inches to the nearest inch. Refer to the figure for Exercises 4 –6. Ramona wants to renovate the kitchen in her house. The figure shows a blueprint of the new kitchen drawn to a scale of 1 cm : 2 ft. Use a centimeter ruler and the figure to find each actual measure in feet. 4. width of the kitchen
5. length of the kitchen
10 ft
14 ft
6. width of the sink
7. area of the pantry
5 ft 9 in. 16 ft 4 in.
3INK
3TOVE
12 ft2
2 ft
0ANTRY
Given that DEFG WXYZ, find each of the following. 7 $ '
0 28 mm ! 40 mm2 10 mm
8
% &
:
8. perimeter of WXYZ 9. area of WXYZ
Copyright © by Holt, Rinehart and Winston. All rights reserved.
15 mm
9
42 mm 90 mm2
36
Holt Geometry
Name LESSON
7-5
Date
Class
Name
Practice A
LESSON
7-5
Using Proportional Relationships
A city engineer wants to check that the height of a roadside sign is within the limits set by city regulations. She decides to use indirect measurement to find the height. She places a yardstick so that it is perpendicular to the ground and measures its shadow. Then she measures the shadow of the sign. Refer to the figure for Exercises 1 and 2. (The figure is not drawn to scale.)
� 3 ft
AC � ___ DF so _3_ � ___ DF; DF � 21 feet ___ EF
BC
�
7
1
�
1 ft �
7 ft
Practice B Using Proportional Relationships
�
triangles. So �ABC � �ADE by AA �. 2. Find the length of the shadow of the second platform in feet and inches to the nearest inch. 3. A 5-foot-8-inch-tall technician is standing on top of the second platform. Find the length of the shadow the scaffold and the technician cast in feet and inches to the nearest inch.
10
20
30
50
40
30
20
10
END ZONE
40
50
4. width of the kitchen
10
20
30
40
4. Find the length of the field from the back of one end zone to the back of the other.
14 feet
�
35
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Name
LESSON
7-5
� � 28 mm � � 40 mm2 10 mm
�
�
�
Class
Holt Geometry
�
15 mm
42 mm 90 mm2
9. area of WXYZ
2
Date
������
�
8. perimeter of WXYZ
2_1_ inches
width �
12 ft
�
�
6. Set up and solve proportions to find the length and width of the pool in the scale drawing.
5 inches
�����
2
Given that DEFG � WXYZ, find each of the following.
An Olympic standard swimming pool is a rectangle that measures 50 meters in length and 25 meters in width. Complete Exercises 6 and 7 to make a scale drawing of an Olympic standard swimming pool, using a scale of 1 in : 10 m.
length �
����
7. area of the pantry
2 feet
120 yards about 53 yards
5. Estimate the width of the field to the nearest yard.
16 feet 4 inches
5. length of the kitchen
6. width of the sink
10 yards
3. Find the distance from the front to the back of an end zone.
5 feet 9 inches
Refer to the figure for Exercises 4 –6. Ramona wants to renovate the kitchen in her house. The figure shows a blueprint of the new kitchen drawn to a scale of 1 cm : 2 ft. Use a centimeter ruler and the figure to find each actual measure in feet.
END ZONE
40
�
� 6 ft 3 in. � _ _
10 feet 30
8 ft 2 in.
�ADE are congruent corresponding angles, and �A is common to both
Use the figure for Exercises 3 –5. The figure shows a scale drawing of a professional football field. The scale of the drawing is 1 cm : 10 yds. Use a centimeter ruler and the figure to find each actual measure in yards.
20
�
Possible answer: Because the sun’s rays are parallel, BC � DE. �ABC and
10 feet
10
� 7 ft 6 in.
1. Explain why �ABC is similar to �ADE. (Hint: The sun’s rays are parallel.)
2. According to city regulations, the maximum height of a roadside sign is 30 feet. Find the length of the shadow of a 30-foot-tall sign at this time of day.
Class
Refer to the figure for Exercises 1–3. A city is planning an outdoor concert for an Independence Day celebration. To hold speakers and lights, a crew of technicians sets up a scaffold with two platforms by the stage. The first platform is 8 feet 2 inches off the ground. The second platform is 7 feet 6 inches above the first platform. The shadow of the first platform stretches 6 feet 3 inches across the ground.
� Famous B-B-Q
1. �ABC � �DEF. Write and solve a proportion to find DF, the height of the sign.
Date
36
Copyright © by Holt, Rinehart and Winston. All rights reserved.
Name
Practice C
LESSON
7-5
Using Proportional Relationships
Date
Class
Holt Geometry
Reteach Using Proportional Relationships
A scale drawing is a drawing of an object that is smaller or larger than the object’s actual size. The drawing’s scale is the ratio of any length in the drawing to the actual length of the object.
A major league baseball infield consists of the four bases, the pitching mound and rubber, and the “skinned” area of clay around the base paths. It is 90 feet between each base, and the angle between bases is 90°. The pitching rubber is 60 feet 6 inches from home plate. The skinned area is an arc with a radius of 95 feet from the pitching rubber.
The scale for the diagram of the doghouse is 1 in : 3 ft. Find the length of the actual doghouse.
1. Make a scale drawing of an infield, using the scale 1 inch : 30 feet. Show all the features described above.
����� ����
0.75 in.
�����
First convert to equivalent units: 1 in : 36 in. (3 ft � 12 in./ft).
� �� � �� ��
�����
diagram length actual length
���� �����
������� �������� ������
������ ����
� �
1 0.75 � 36 x
� diagram length � actual length
1x � 36(0.75)
Cross Products Property
x � 27 in.
Simplify.
The actual length of the doghouse is 27 in., or 2 ft 3 in.
�����
�����
The scale of the cabin shown in the blueprint is 1 cm : 2 m. Find the actual lengths of the following walls.
����� ����
_
_
1. HG
2. GL
6m _
���� ����
����
����
3. The volume of a solid is equal to length times width times depth. 3 Volume is expressed in cubic units (for example, ft ). Find the volume of each solid. 4. Find the ratio of the volumes in simplest form.
5. 1 in : 1 ft
24 ft3; 375 ft3 8 : 125 or 125 : 8
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�
6. 1 in : 2 ft
45 in. by 28 in.
22.5 in. by 14 in.
7. 1 in : 3 ft
8. 1 in : 6 ft 8 in.
15 in. by 9 _1_ in. 3
The ratio of the volumes is the cube of the similarity ratio. 37
�
A rectangular fitness room in a recreation center is 45 feet long and 28 feet wide. Find the length and width for a scale drawing of the room, using the following scales.
5. Tell what relationship there is between the ratio of the volumes and the similarity ratio of the two prisms
Copyright © by Holt, Rinehart and Winston. All rights reserved.
1m
������
2 : 5 or 5 : 2
2. Find the similarity ratio of the two prisms.
10 m 4. JM
7m
�����
�
�
_
3. HJ So far you have learned about similar polygons. Threedimensional objects can also be similar. The figure shows two similar rectangular prisms. Use the figure for Exercises 2 –5.
�
�
Holt Geometry
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59
6.75 in. by 4.2 in. 38
Holt Geometry
Holt Geometry
