Question 1
1(a):
Choose the correct definition for the term ‘similar shape’.
ANSWER: Multiple Choice (Type 1)
A: Similar shapes have the same number of sides
B: Similar shapes have sides all the same length
C: Similar shapes are shapes that have been rotated
D: Similar shapes are enlargements of each other
Answer: D
Workings:
Similar shapes have the same sized angles but side lengths that have changed by the same scale amount.
Marks = 1
1(b):
Using the shapes above, find a triplet of similar shapes
ANSWER: Multiple Choice (Type 1)
A: C, A, D
B: A, G, F
C: J, K, L
D: C, H, B
Answer: C
Workings:
Shapes J, K and L are all circles, but are of different sizes so must be enlargements of each other. There are no angles in a circle so they must be similar shapes.
Marks = 1
Question 2
The diagram below shows a variety of triangles.
In the set of shapes there are two pairs of similar triangles and one triplet of similar triangles.
2(a):
From the shapes above identify which of the following is a pair of similar triangles
ANSWER: Multiple Choice (Type 1)
A: B & G
B: A & F
C: D & E
D: C & B
Answer: B
Workings:
From the information given, we know shapes A and F are equilateral triangles.
This must mean that all their angles are , so regardless of the side lengths, they are similar shapes.
Marks = 1
2(b):
From the shapes above identify which of the following is a pair of similar triangles
ANSWER: Multiple Choice (Type 1)
A: G & H
B: A & D
C: C & F
D: B & E
Answer: D
Workings:
Shapes B and E are both isosceles with a right angle, so the base angles must be in both diagrams.
This means that, regardless of their side lengths, they are similar shapes.
Marks = 1
2(c):
From the shapes above identify which of the following is a triplet of similar triangles
ANSWER: Multiple Choice (Type 1)
A: E, D, F
B: C, D, H
C: A, B, H
D: B, F, G
Answer: B
Workings:
Shapes C, D and H are all right angled triangles.
We are given corresponding lengths for each side that are increased by the same scale factor.
The sides in shape C are the side lengths in shape D.
The sides in shape H are the side lengths in shape D.
Therefore the angles must stay the same and the shapes are similar.
Marks = 1
Question 3
The two triangles, ABC and DEF shown below are similar.
3(a):
What is the scale factor that transforms ABC to DEF?
ANSWER: Simple Text Answer
Answer: 3
Workings:
Find the scale factor by dividing the 42 cm side in the right-hand shape by the 14 cm side in the left-hand shape as they are corresponding sides.
Marks = 1
3(b):
Hence, or otherwise, calculate length EF in cm
ANSWER: Simple Text Answer
Answer: 36
Workings:
The corresponding side in the left-hand shape is 12 cm
Increasing by scale factor 3 means
Marks = 1
3(c):
Hence, or otherwise, calculate length AC in cm
ANSWER: Simple Text Answer
Answer: 17
Workings:
Use to get from the right-hand shape to the left-hand shape.
Marks = 1
Question 4
In the diagram below the triangles XCD and XAB are similar.
4(a):
What is the scale factor of the triangles?
ANSWER: Simple Text Answer
Answer:
Workings:
and are matching sides
Dividing by gives the scale factor
Marks = 1
4(b):
Using the scale factor, calculate XC in cm
ANSWER: Simple Text Answer
Answer: 21
Workings:
Marks = 1
4(c):
Given that , find the values of AX and XD in cm.
ANSWER: Multiple Answers (Type 1)
Answer: ,
Workings:
Marks = 2
Question 5
Triangles and are mathematically similar.
5(a):
What is the scale factor that transforms ABC to BDE?
ANSWER: Simple Text Answer
Answer: 2
Workings:
Marks = 1
5(b):
Use the scale factor to calculate the length of BE and DE.
ANSWER: Multiple Answers (Type 1)
Answer: ,
Workings:
Marks = 2
Question 6
ABCD and AGFE are mathematically similar
6(a):
What is the scale factor of ADCB to AEFG?
ANSWER: Simple Text Answer
Answer: 3
Workings:
Marks = 1
6(b):
The area of ABDC is 24 .
Calculate the area of AEFG in .
ANSWER: Simple Text Answer
Answer: 216
Workings:
Scale Factor for area is Scale Factor squared for side length
Marks = 2
Question 7
In the diagram below, IJKH and ILMH are mathematically similar.
IJ=5 cm
HM=20 cm
Find the scale factor of IJKH to ILMH.
ANSWER: Simple Text Answer
Answer: 2
Workings:
Recognise is an enlargement of and that is an enlargement of
and are the same length so let
Rearranging gives
Substituting this gives as the Scale Factor
Marks = 3