Enlargement and similarity exemplar questions and answers

1.

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2.

Rosie has enlarged a photograph of her and Tommy.
Is her enlargement correct?
How do you know?
Can you prove your answer?
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3.

Rosie has enlarged a photograph of her and Tommy.
Is her enlargement correct?
How do you know?
No, The picture has been
stretched vertically but not
horizontally.
Can you prove your answer?
Yes, if the enlargement is correct then the ratio of the
side lengths will be equal in each picture.
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4.

Which triangles are similar?
How can you tell?
Create another triangle similar to triangle A with side lengths
Greater than 10
Less than 1
A
B
C
D
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5.

Which triangles are similar? A, B and D
How can you tell?
Corresponding sides are the in the same ratio.
Create another triangle similar to triangle A with side lengths
Greater than 10
Less than 1
A
B
C
D
Compare examples as a class.
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6.

Whitney says that triangle A and B are similar.
Do you agree? Explain why?
A
B
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7.

Whitney says that triangle A and B are similar.
Do you agree? Explain why?
Yes, B is an enlargement of A
using a scale factor of 2.
A
B
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8.

Enlarge each shape by scale factor 3
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9.

Enlarge each shape by scale factor 3
Compare answers as a class.
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10.

What is the greatest integer scale factor that shape A
can be enlarged by so that it fits on the grid?
A
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11.

What is the greatest integer scale factor that shape A
can be enlarged by so that it fits on the grid?
A
Greatest integer scale factor is 2
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12.

A regular hexagon has been enlarged by scale factor 4
The image has a perimeter of 36 cm.
What is the length of each side of the object?
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13.

A regular hexagon has been enlarged by scale factor 4
The image has a perimeter of 36 cm.
What is the length of each side of the object?
Side length = 24 cm
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14.

X is 2 cm away from the midpoint of AC.
Enlarge triangle ABC by scale factor 2 about the point X.
A
X
C
B
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15.

X is 2 cm away from the midpoint of AC.
Enlarge triangle ABC by scale factor 2 about the point X.
A
X
C
B
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16.

Rectangle A has been enlarged by scale factor 2 from P.
Tommy and Whitney compare their methods.
A’
A’
I scaled the distances
between the centre and
corresponding vertices.
2
1
2
4
I used the rays method.
Which method do you prefer?
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17.

Rectangle A has been enlarged by scale factor 2 from P.
Tommy and Whitney compare their methods.
A’
A’
I scaled the distances
between the centre and
corresponding vertices.
2
1
2
4
I used the rays method.
Which method do you prefer?
Discuss methods as a class
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18.

Annie enlarges shape L from (−3, 3) with scale factor 2
The image will be
positioned equally
between the 1st, 3rd
and 4th quadrants.
Show that Annie is wrong.
Find a centre of enlargement that would make Annie’s claim true.
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19.

Annie enlarges shape L from (−3, 3) with scale factor 2
The image will be
positioned equally
between the 1st, 3rd
and 4th quadrants.
Show that Annie is wrong.
Find a centre of enlargement that would make Annie’s claim true.
(−4, 4)
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20.

Match up the cards of equal value.
1.5 × 8
3
of 12
4
4
of 10
5
One third
of 9
4
×9
3
1
of 8
2
3
of 2
2
2
6×
3
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21.

Match up the cards of equal value.
1.5 × 8
3
of 12
4
4
of 10
5
One third
of 9
4
×9
3
1
of 8
2
3
of 2
2
2
6×
3
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22.

1
Draw an enlargement of the rectangle by scale factor
3
A shape can only be enlarged by a
fractional scale factor if the
denominator of the fraction is a factor
of the side lengths.
12 cm
6 cm
Explain why Amir is incorrect.
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23.

1
Draw an enlargement of the rectangle by scale factor
3
4 cm
2 cm
12 cm
A shape can only be enlarged by a
fractional scale factor if the
6 cm
denominator of the fraction is a factor
of the side lengths.
Explain why Amir is incorrect.
The rectangle may have non-integer lengths but still be
an enlargement.
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24.

A triangle has vertices (2, 4), (10, 2) and (8, 0).
1
Enlarge the triangle by scale factor
2
about the origin
about the point (8, 2)
about the point (−2, −2)
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25.

A triangle has vertices (2, 4), (10, 2) and (8, 0).
1
Enlarge the triangle by scale factor
2
Vertices - (1, 2), (5, 1), (4,0)
about the origin
about the point (8, 2)
Vertices - (5, 3), (9, 2), (8,1)
about the point (−2, −2) Vertices - (0, 1), (4, 0), (3,−1)
Compare accuracy of answers as a class.
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26.

Use the rays to enlarge the pentagon by scale factor −2
from the point.
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27.

Use the rays to enlarge the pentagon by scale factor −2
from the point.
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28.

Enlargements by a positive scale
factor are larger than those by a
negative scale factor.
Is Dexter’s claim always, sometimes or never true?
Justify your answer
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29.

Enlargements by a positive scale
factor are larger than those by a
negative scale factor.
Is Dexter’s claim always, sometimes or never true?
Justify your answer
Dexter claim is sometimes true. It depends on the
magnitude of the scale factor, for example:
• Scale factors of −5 and 3. The scale factor −5
produces a larger enlargement
• Scale factors of 5 and −3. The scale factor 5
produces a larger enlargement
• Scale factors of −3 and3. Both produce the same
sized enlargement
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30.

Enlarge triangle ABC with scale factor −1 from each of the
centres of enlargement
(0, 0)
(−1, 1)
(−2, −1)
With which of the centres would an enlargement of scale
factor −2 still fit on the grid?
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31.

Enlarge triangle ABC with scale factor −1 from each of the
centres of enlargement
B
(0, 0)
A
(−1, 1)
(−2, −1)
C
With which of the centres would an enlargement of scale
factor −2 still fit on the grid?
Triangle C
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32.

Identify the scale factor between each pair of shapes and
find any missing information.
3.5 cm
4.2 cm
10.5 cm
12 cm
? cm
?°
? cm
40°
18 cm
4 cm
? cm 40°
63° 12 cm
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33.

Identify the scale factor between each pair of shapes and
find any missing information.
3.5 cm
10.5 cm
4.2 cm
Scale Factor = 3
12 cm
12.6 cm
63°
6 cm
40°
18 cm
4 cm
? cm 40°
63° 12 cm
Scale Factor = 1.5
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34.

Rectangles G and H are similar.
Eva thinks the missing length in H is 9
Do you agree? Justify your answer
?
3 cm
4 cm
G
12 cm
H
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35.

Rectangles G and H are similar.
Eva thinks the missing length in H is 9
Do you agree? Justify your answer
?
3 cm
4 cm
G
12 cm
H
No, the corresponding side length on G is 4 cm
because the rectangle has been rotated.
The missing side length is 16 cm
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36.

ABCD and ABEF are similar isosceles trapezia.
∠DAE = 28° and ∠BCD = 104°
Work out ∠AEF
The ratio of AB:DC is 2 : 3
Work out the ratio of EF: DC
A
D
B
E
F
C
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37.

ABCD and ABEF are similar isosceles trapezia.
∠DAE = 28° and ∠BCD = 104°
A
Work out ∠AEF
∠AEF= 104°
The ratio of AB:DC is 2 : 3
E
D
Work out the ratio of EF: DC
B
F
C
EF : DC = 4 : 9
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38.

Triangles A and B are similar.
1.8 cm
1.97 cm
A
7.2 cm
100°
35°
11 cm
What’s the scale factor of enlargement from triangle A to triangle B?
35°
Work out the missing angles.
Work out the missing lengths.
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39.

Triangles A and B are similar.
100°
7.2 cm
7.89 cm
1.97
cm
100°
1.8 cm
A
45°
35°
45°
35°
2.75 cm
11 cm
What’s the scale factor of enlargement from triangle A to triangle B?
Scale factor = 4
Work out the missing angles.
Work out the missing lengths.
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40.

The two triangles are similar.
Which sides in triangle ABC correspond to which sides
in triangle PQR?
Which sides and angles can you work out?
R
A
x
10 m
x B
20 m
6m
C
P
15 m
Q
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41.

The two triangles are similar.
Which sides in triangle ABC correspond to which sides
in triangle PQR? AC corresponds to PQ
BC corresponds to RQ
AB corresponds to RP
Which sides and angles can you work out?
R
A
x
10 m
x B
20 m
6m
C
Scale factor = 2.5
BC = 8 m RP = 25 m
P
15 m
Q
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42.

Show that triangles ABC and CDE are similar.
The perimeter of ABC is 36 m.
Find the missing lengths in ABC and CDE.
A
12 m
C
B
6m
D
8m
E
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43.

Show that triangles ABC and CDE are similar.
The perimeter of ABC is 36 m.
Find the missing lengths in ABC and CDE.
A
12 m
C
B
6m
D
8m
E
12
Scale factor = = 1.5
8
BC = 6 × 1.5 = 9 m
AB = 36 − 21 = 15 m
DE = 15 ÷ 1.5 = 10 m
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44.

In each triangle, label the hypotenuse and the
sides opposite and adjacent to the 30° angle.
30°
30°
30°
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45.

In each triangle, label the hypotenuse and the
sides opposite and adjacent to the 30° angle.
opposite
adjacent
30°
hypotenuse
hypotenuse
opposite
adjacent
30°
adjacent
30°
hypotenuse
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46.

Work out the ratio of the length of sides opposite the given
angle and the hypotenuse in each triangle. Investigate other
triangles similar to these.
1 cm
15 mm
30 mm 30° 25.9 mm
4.2 m
3 cm
2.1 m
30° 2 cm
30°
3.64 m
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47.

Work out the ratio of the length of sides opposite the given
angle and the hypotenuse in each triangle. Investigate other
triangles similar to these.
1 cm
15 mm
30 mm 30° 25.9 mm
4.2 m
3 cm
2.1 m
30° 2 cm
30°
3.64 m
Ratio = 1 : 2 for all triangles.
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48.

In which triangles is the angle labelled