Unit 19 Section 2 : Similar shapes
Similar shapes are those which are enlargements of each other; for example, the
three triangles shown below are similar:
For example, to get triangle A from triangle C we enlarge it by multiplying all the sides by a scale factor of 2.
Similarly, we can get triangle C from triangle A by multiplying each side by a scale factor of ½.
Triangles A and C are therefore enlargements of each other, and as such are similar.
Finding the scale factor
Often we will want to find the scale factor needed to between two shapes. There is a simple way to do this.
Firstly you need to find a corresponding side in each shape where you know the length of both.
Next you need to divide the length in the shape you are going to by the length in the shape you are coming from.
For example, in triangles A and B above, the bottom sides 6cm and 9cm correspond to each other.
To find the scale factor from A to B, we divide the length in B by the length in A.
You can see that 9 ÷ 6 = 1.5, so the scale factor from A to B is 1.5.
Similarly, to find the scale factor from B to A, we divide the length in A by the length in B.
Now we can see that 6 ÷ 9 = ^{2}/_{3} so the scale factor from B to A is ^{2}/_{3}.
Practice Question
The following diagram shows two similar shapes:

Work out the answer to each of these questions then click on the button marked
to see whether you are correct.
(a) What is the scale factor from Triangle 1 to Triangle 2?
(b) What is the length of side DF?
(c) What is the scale factor from Triangle 2 to Triangle 1?
(d) What is the length of side BC?

Exercises
Work out the answers to the questions below and fill in the boxes. Click on the
button to find out whether you have answered correctly. If you are right
then will appear and you should move on to the next
question. If appears then your answer is wrong. Click
on to clear your original answer and have another go.
If you can't work out the right answer then click on
to see
the answer.
You have now completed Unit 19 Section 2
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