Symmetry and Similarity Review
Short Answer
1. Determine the scale factor for this scale drawing.
Original Scale diagram
diagram
2. Determine the scale factor for this scale drawing.
Original
diagram
Scale diagram
3. Which of trapezoids A, B, C, and D are scale diagrams of trapezoid O?
O
A
B
C
D
4. A square has side length 4.3 cm.
The square is enlarged by a scale factor of 3.4.
Determine the side length of the enlargement.
5. A circle has diameter 48 cm. The diameter of the reduction is 42 cm.
Determine the scale factor of the reduction as a fraction and as a decimal.
.
6. Determine the scale factor for each reduction.
a) Quadrilateral B is a reduction of quadrilateral A.
b) Quadrilateral C is a reduction of quadrilateral A.
c) Quadrilateral B is a reduction of quadrilateral C.
B
A
C
7. Determine the value of y in this proportion:
8. These quadrilaterals are similar. Determine the value of x.
21 cm
14 cm
x
42 cm
9. These quadrilaterals are similar. Determine the values of x and y°.
13.6
31°
10.2
15.3
x
y°
10. Quadrilateral PQRS is similar to quadrilateral ABCD.
If AB = 3 cm, BC = 4 cm, and QR = 8.96 cm, determine the length of PQ.
11. Determine the length of EF in these similar triangles.
A
D
9
C
B 16.2
18
F
E
12. Determine the length of BD in these similar triangles.
A
B
C
20
7
D
10.5
E
13. Determine the length of RS in these similar triangles.
P
14 m
Q
159.6 m
R
T 19 m
S
14. Determine the length of NO in these similar triangles.
N
L
3.9 cm
P 4.8 cm
M
12.8 cm
O
15. This polygon is one-half of a shape. Use the dotted line as a line of symmetry to complete the shape by
drawing its other half.
y
6
5
4
3
2
1
1
2
3
4
5
6
7
x
16. Identify the pentagons that are related to the black pentagon by a line of reflection.
Describe the position of each line of symmetry.
y
11
10
9
R
8
7
6
5
4
P
S
3
2
Q
1
1
2
3
4
5
6
7
8
9 10 11 12 13 x
17. Draw the rotation image after rotating the shape 90° clockwise about P.
P
18. What is the order of rotational symmetry and angle of rotation symmetry for this design?
19. Describe the rotational symmetry and line symmetry of this design.
20. Which of triangles A, B, and C are related to the shaded triangle by rotational symmetry about the origin?
y
5
4
3
B
2
1
–5 –4 –3 –2 –1
–1
C
–2
1
2
3
4
5
x
A
–3
–4
–5
21. Determine whether polygon A and its image are related by line symmetry after each transformation:
i) a translation R3
ii) a translation U6
iii) a reflection in a vertical line through 4 in the x-axis
iv) a reflection in a horizontal line through 7 in the y-axis
y
13
12
11
10
9
8
7
6
5
4
3
A
2
1
1
2
3
4
5
6
7
8
x
Problem
22. Determine each scale factor.
a) Square TPQR is a scale drawing of square TABC.
b) Square TGHK is a scale drawing of square TDEF.
c) Square TPQR is a scale drawing of square TDEF.
d) Square TLMN is a scale drawing of square TABC.
Q
P
M
L
H
G
E
D
A
T
B
C
F
K
N
R
23. Calculate the values of the variables in this proportion:
24. 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?
y
5
4
3
2
1
–6 –5 –4 –3 –2 –1
–1
–2
–3
–4
–5
1
2
3
4
5
6
x
Symmetry and Similarity Review
Answer Section
SHORT ANSWER
1. ANS:
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
2. ANS:
The scale factor is 3.5.
PTS: 1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
3. ANS:
Trapezoids C and D
PTS: 1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
4. ANS:
14.62 cm
PTS: 1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
5. ANS:
PTS: 1
DIF: Easy
REF: 7.2 Scale Diagrams and Reductions
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
6. ANS:
a)
b)
c)
PTS: 1
DIF: Moderate
REF: 7.2 Scale Diagrams and Reductions
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
7. ANS:
0.45
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
8. ANS:
x = 28 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
9. ANS:
x = 20.4
y° = 31°
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
10. ANS:
PQ = 6.72 cm
PTS: 1
DIF: Moderate
REF: 7.3 Similar Polygons
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Procedural Knowledge
11. ANS:
EF = 32.4
PTS: 1
DIF: Easy
REF: 7.4 Similar Triangles
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Procedural Knowledge
12. ANS:
BD = 8
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
13. ANS:
RS = 117.6 m
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
14. ANS:
10.4 cm
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
15. ANS:
y
6
5
4
3
2
1
1
2
3
4
5
6
7
x
PTS: 1
DIF: Easy
REF: 7.5 Reflections and Line Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
16. ANS:
Pentagon P is the reflection image of the black pentagon in the vertical line through 3 on the x-axis.
Pentagon Q is the reflection image of the black pentagon in the horizontal line through 3 on the y-axis.
Pentagon R is the reflection image of the black pentagon in the oblique line through
(4, 10) and (12, 2).
Pentagon S is the reflection image of the black pentagon in the vertical line through 7.5 on the x-axis.
PTS: 1
DIF: Moderate
REF: 7.5 Reflections and Line Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Conceptual Understanding | Communication
17. ANS:
P
PTS: 1
DIF: Easy
REF: 7.6 Rotations and Rotational Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
18. ANS:
4; 90°
PTS: 1
DIF: Moderate
REF: 7.6 Rotations and Rotational Symmetry
LOC: 9.SS5
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
19. ANS:
Rotational symmetry of order 4 about the centre
4 lines of symmetry through the centre
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
20. ANS:
Triangles A and B
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
21. ANS:
i) There is no line of symmetry.
ii) The line of symmetry is the horizontal line through 6 on the y-axis.
iii) The line of symmetry is the vertical line through 4 on the x-axis.
iv) The line of symmetry is the horizontal line through 7 on the y-axis.
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
PROBLEM
22. ANS:
a) The scale factor is:
b) The scale factor is:
c) The scale factor is:
d) The scale factor is:
PTS: 1
DIF: Moderate
REF: 7.1 Scale Diagrams and Enlargements
LOC: 9.SS4
TOP: Shape and Space (Transformations)
KEY: Procedural Knowledge
23. ANS:
PTS: 1
DIF: Moderate
REF: 7.3 Similar Polygons
LOC: 9.SS3
TOP: Shape and Space (3-D Objects and 2-D Shapes)
KEY: Procedural Knowledge
24. ANS:
6
y
5
4
3
2
1
–7 –6 –5 –4 –3 –2 –1
–1
1
2
3
4
5
6
7 x
–2
–3
–4
–5
–6
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