Chapter

Chapter
1. Sage is using flat stones like these to build a walkway.
12 cm
P
44o
16 cm
Q
132o
18 cm
D
14 cm
E
132o
21 cm
44o
54o R
130o
10 cm
S
54o
24 cm
130o
G
F
15 cm
a) Measure and label the corresponding angles on the
polygons.
b) Complete the chart for the given measures of
corresponding sides of polygons PQRS and DEFG.
Sides of PQRS
Corresponding
sides of DEFG
PQ =
12
cm
QR =
14
cm
RS =
10
cm
SP =
16
cm
DE = 18 cm EF = 21 cm FG = 15 cm GD = 24 cm
c) Calculate ratios for corresponding sides of DEFG and PQRS.
AW10
0-17-650271-8
Figure Number
Company
Technical
DE
18 cm
=
, or
PQ
12 cm
1.5
15 cm
FG
=
, or
RS
10 cm
1.5
21 cm
EF
=
, or
QR
14 cm
1.5
24 cm
GD
=
, or
SP
16 cm
1.5
d)
Are the stones similar? How do you know?
C09-F49b-AW10.eps
e.g., Yes, DEFG ~ PQRS. The corresponding angles are
equal and the ratios of corresponding sides are equal.
Pass
1st Pass
Approved
e) What is the scale factor for using PQRS to calculate
lengths for DEFG? 1.5
Not Approved
2. Are all equilateral triangles similar? Explain how you know.
e.g., Yes. The sum of the angles in any triangle is 180o. An
equilateral triangle has three equal angles, so each angle is
180o 4 3 = 60o. Triangles with three pairs of equal
corresponding angles are similar.
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3. Draw a similar triangle using a scale factor of 140%. Label the
angle measures and side lengths in your triangle.
105°
25°
20 mm
50°
49 mm
105o
35 mm
28 mm
45 mm
50o
25o
63 mm
4. This is a floor plan for the MacBride
Museum of Yukon History in Whitehorse.
Cyr is planning to take a group from a
daycare to the Discovery Zone and
wants to know its size.
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Men
Women
1
Taylor
& Drury
Room
22 m
1 cm on the map represents
2.75 m.
AW10
Natural World Gallery
Downstairs
a) How many centimetres on the map
equal 22 m? 8.0 cm
b) What actual distance would 1 cm
on the map represent?
8.0 cm represents 22 m, so
22 m ÷ 8.0 5 2.75 m
3
4
Discovery
Zone
Gift
Shop
Log Building
Entrance
The actual length and width are about 5.1 m and
about 5.4 m.
Technical
C09-F51b-AW10.eps
c)
What are the actual length and width of the Discovery Zone?
e.g., On the floor plan, it is 1.5 cm by 1.6 cm; actual
Pass
1st Pass
Figure Number
Company
Approved
Not Approved
Mining
History
measurements are about 1.5 x 2.75 m = 4.125 m and
1.6 x 2.75 m = 4.4 m.
5. a) How can you tell that ΔABC ~ ΔEDC?
e.g., ∠DCE = ∠BCA because they’re opposite angles.
∠CAB = ∠AW10
CED because they’re 90 . So ∠EDC must
A 20 cm B
20 cm
o
C
15 cm
0-17-650271-8
equal ∠ABC
; soNumber
the triangles
are similar.
Figure
C09-F52-AW10.eps
Company
D
b) How long is
side ED?
Technical
>
E
>
Pass and CE are 2nd
Pass
e.g., Sides CA
corresponding
sides and
Approved
20
the ratio isNot15Approved
, so the ratio for other corresponding
sides must be
20
15 .
Side AB = 20 and it corresponds to side
ED, so ED must be 15 cm long.
Copyright © 2011 by Nelson Education Ltd.
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Chapter 9 Similar Polygons
263
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