ANSWERS
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Practice
2-8
2-8
Proportions and Similar Figures
The figures in each pair are
1. AABC
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—
Proportions and Sin
r Figures
12. Sammy is constructing a model bridge out of sticks. The actual bridge is
1320 ft long. He wanis the scale of his bridge to he 1 :400. How iong should the
model be?
3.3 in.
Identify the corresponding sides and angles.
2. QRST - tmvx
ADEF
Practice (continued)
13. The Finish-Line Company is drawing up plans for a room addition shown
below. The addition will include a large bedroom with a bathroom as shown.
Afl and Df,fiCand EF, AC and
DF, LA and ZD, Z.B and LE,
LC and Z.F
ffS and VW, ST and WX, TQ and XU, Qfl
and UV. LR and i!V, /IS and LW, LT
and zJf, ,dQand LU
The figures in each pair are similar. Find the missing length.
T 3 ft
a. What are the actual dimensions of the room addition?
24.99 ft by 15 ft
b. What are the acnial dimensions of the bathroom?
about 8 ft by 10 ft
c. What is the actual length of the exterior wall between the end of the room
addition and the bathroom wall? This length is represented by x.
about 17 ft
14. Writing Are all right triangles similar? Explain your answer.
Answers may vary. Sample: no; the right triangles formed by the
diagonal in a square are not similar to the triangles found by the
diagonal in a rectangle that is not a square.
15. Writing A pizza shop sells small 6 in. pizzas and medium 12 in. pizzas.
Shouid the medium pizzas cost twice as much as (he small pizzas because
they are twice the size? Explain.
The radius of the small pizza is 3 in., so its area is 9*. The radius of the larger
pizza is 6 in., so its area is 16*. They should charge four times as much.
The scale oTa map is 0.5 in.: 20 mi. Find (he actual distance corresponding to
each map distance.
10. A museum has a wax sculpture of a historical village. J lie scale is 1.5 : 8. If the
height of a hut in the sculpture is 5 feet, how tall was the original hut to the
it whole foot? about 27 ft
11. On a map. (he length of a river is 4.75 in. The actual length of the rl
247 miles. What is the scale of the map? -LiiL
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2-8
Page 76
Practice
2-8
Proportions and 5imilar Figures
0
and
LE, LB andLF,_LC
and
LG,
LD a n d Z ^ AB and EF, BC and FG, CD
and GH, AD and EH
Proportions and Similar Figures
Hie scale of a map is 0.25 cm : 15 km. Find the actual distance corresponding to
each map distance.
6. 0.75 cm 45 km
7. 2 cm 120 km
The figures in each pair are similar. Identify the corresponding sides and angles.
1. ABCD - EFCH
2. AAfJVO - APQR
LA
Practice (continued)
. 3.5cm 210 km
P
and LP^ LN and LQ, LO
and LRj AWjmd PQ, NO and
OR. MO and PR
LM
9. r>.'Jr>cm 315 km
10. For a celebration a town is going to pass out miniature replicas of the town's
bell. The replicas are 9 in. tall. If the scale of the replica is 1 in.: 0.5 ft, how tall
is the actual bell? 4.5 ft
The figures in each pair are similar. Find the missing length.
11. An architect created a scale model of what a college campus will look like
once construction is finished. The scale for die model is 2 in.: 25 ft. The talle;
building in the model is 10 in. tali. How tall is (he actual building? 1 IS t
12. A model of a golf course says that hole #9 is 173 yards long. If the scale of the
model is 2 in.: 20 yards, how many inches are there between the tee and (he
hole on the mode!? 17.5 in.
13. Open-Ended Give an example of similar figures in your school.
Answers may vary. See students' work.
14. Reasoning You are given two similar triangles. You know that one pair
of corresponding sides is equal. What do you know about the other sides?
Explain.
The other sides are also equal. Since the corresponding angles
and one pair of corresponding sides is equal, the scale is 1 ; 1.
The other pairs of corresponding sides are also equal.
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