Name: ______________________
Class: _________________
Date: _________
ID: A
Math 9 Unit 7 Similarity and Transformations Practice Exam
Name: ______________________
ID: A
4. How many lines of symmetry does this tessellation have?
Short Answer
1. A soccer pitch is about 90 m long. A model of the soccer pitch is made using a scale of 1:70. Determine
the length of the model to the nearest centimetre, if necessary.
2. Determine the length of EB in this pair of similar triangles.
5. Which example shows a reflection of triangle X in the dotted line?
3. Determine the measure of !KML in this pair of similar triangles.
6. What is the order of rotational symmetry and angle of rotation symmetry for this design?
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2
Name: ______________________
ID: A
Name: ______________________
ID: A
7. Which figure shows the rotation image of pentagon A after a 216° clockwise rotation about its centre?
12. These quadrilaterals are similar. Determine the value of x.
8. Which of the following letters have both rotational symmetry and line symmetry?
13. These parallelograms are similar. Determine the values of x° and y.
9. Which of trapezoids A, B, C, and D are scale diagrams of trapezoid O?
14. Triangle KLM is similar to "RST.
The corresponding angles are: !K = !R, !L = !S, !M = !T
State the ratios of the corresponding sides.
15. Describe a rotation that makes parallelogram QRST a rotation image of parallelogram ABCD.
10. A square has side length 5.3 cm.
The square is enlarged by a scale factor of 4.5.
Determine the side length of the enlargement.
11. Is "PQR a scale diagram of "ABC? If yes, state the scale factor.
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4
Name: ______________________
ID: A
16. The design below is created after trapezoid ABCD is rotated 90° clockwise about the origin, 180° about
the origin, and 90° counterclockwise about the origin. Identify any symmetry in the design.
Name: ______________________
ID: A
19. Square B is a reduction of square A. Determine the scale factor.
20. These quadrilaterals are similar.
17. Write a complete word using upper case letters that has horizontal symmetry. You can use a letter more
than once.
.
a) Determine the values of x and y.
b) If p° = 64°, determine the value of q°.
Problem
18. Determine each scale factor as a fraction.
a) Rectangle PQRC is a scale drawing of rectangle TABC.
b) Rectangle LMNC is a scale drawing of rectangle DEFC.
c) Rectangle LMNC is a scale drawing of rectangle GHKC.
d) Rectangle PQRC is a scale drawing of rectangle GHKC.
e) Rectangle GHKC is a scale drawing of rectangle TABC.
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21. This polygon is part of a larger shape.
Draw the image of the polygon after each reflection:
i) a reflection in the y-axis
ii) a reflection in the x-axis
iii) a reflection in the oblique line through (–5, 5) and (5, –5)
How many lines of symmetry does the shape have?
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ID: A
Math 9 Unit 7 Similarity and Transformations Practice Exam
Answer Section
ID: A
8. ANS:
H, O, X
PTS: 1
DIF: Easy
REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
9. ANS:
Trapezoids C and D
SHORT ANSWER
1. ANS:
129 cm
PTS: 1
DIF: Moderate
REF: 7.2 Scale Diagrams and Reductions
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
2. ANS:
10
PTS: 1
DIF: Moderate
REF: 7.4 Similar Triangles
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Procedural Knowledge
3. ANS:
40°
PTS: 1
DIF: Moderate
REF: 7.4 Similar Triangles
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Conceptual Understanding | Procedural Knowledge
4. ANS:
2
PTS: 1
DIF: Easy
REF: 7.5 Reflections and Line Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Conceptual Understanding
5. ANS:
Example iv
PTS: 1
DIF: Easy
REF: 7.5 Reflections and Line Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
6. ANS:
4; 90°
PTS: 1
DIF: Easy
REF: 7.6 Rotations and Rotational Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
7. ANS:
Figure iii
PTS: 1
DIF: Moderate
REF: 7.6 Rotations and Rotational Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
1
PTS:
LOC:
KEY:
10. ANS:
23.85
1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
9.SS4
TOP: Shape and Space (Transformations)
Procedural Knowledge
cm
PTS: 1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
11. ANS:
Yes, "PQR is a scale diagram of "ABC.
The scale factor is 2.
PTS: 1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
12. ANS:
x = 24 cm
PTS: 1
DIF: Easy
REF: 7.3 Similar Polygons
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Procedural Knowledge
13. ANS:
y=7
x° = 66°
PTS: 1
DIF: Moderate
REF: 7.3 Similar Polygons
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Conceptual Understanding | Procedural Knowledge
14. ANS:
KL LM KM
=
=
RS
ST
RT
PTS: 1
DIF: Easy
REF: 7.4 Similar Triangles
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Conceptual Understanding
2
ID: A
ID: A
15. ANS:
Sample answers:
90° clockwise about the point (4, 4)
90° counterclockwise about the point (4, 4)
270° clockwise about the point (4, 4)
270° counterclockwise about the point (4, 4)
19. ANS:
Square A has area 169 cm2 , so its side length is 13 cm.
Square B has area 25 cm2 , so its side length is 5 cm.
5 cm
5
The scale factor is:
=
13 cm 13
PTS: 1
DIF: Moderate
REF: 7.6 Rotations and Rotational Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Conceptual Understanding | Communication
16. ANS:
The diagram has rotational symmetry of order 4 about the origin and 4 lines of symmetry: the x-axis,
the y-axis, the line through (–4, –4) and (4, 4), and the line through (4, –4) and (–4, 4)
PTS: 1
DIF: Moderate
REF: 7.2 Scale Diagrams and Reductions
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Problem-Solving Skills
20. ANS:
a)
x
10.5
y
7
=
=
5.4
7
13.5
10.5
PTS: 1
DIF: Moderate
REF: 7.7 Identifying Types of Symmetry on the Cartesian Plane
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge | Communication
17. ANS:
Answers will vary
PTS: 1
5.4 #
x
10.5
= 5.4 #
5.4
7
x=
13.5 #
5.4 # 10.5
7
x = 8.1
So, x = 8.1 cm.
y
7
= 13.5 #
13.5
10.5
y=
13.5 # 7
10.5
y=9
So, y = 9 cm.
b) Since corresponding angles in similar polygons are equal, q° = 64°.
PROBLEM
PTS: 1
DIF: Moderate
REF: 7.3 Similar Polygons
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Conceptual Understanding | Procedural Knowledge
18. ANS:
a) The scale factor is:
b) The scale factor is:
c) The scale factor is:
d) The scale factor is:
e) The scale factor is:
PQ
TA
LM
DE
LM
GH
PQ
GH
GH
TA
=
=
=
=
=
2
6
3
=
5
3
4.5
2
4.5
4.5
6
1
3
=
=
=
2
3
4
9
3
4
PTS: 1
DIF: Moderate
REF: 7.2 Scale Diagrams and Reductions
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
3
4
ID: A
21. ANS:
The shape has four lines of symmetry.
PTS: 1
DIF: Moderate
REF: 7.5 Reflections and Line Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Problem-Solving Skills | Procedural Knowledge
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