1. Congruent and similar shapes
Congruent shapes
Similar shapes

2. Congruent shapes

3. 1. Which of these shapes are congruent to the yellow one?
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1. Which of these shapes are congruent to the yellow one? 1 4 3 2 5 7 8 6
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Answers

4. Congruent shapes are all shown in yellow – were you right?
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Congruent shapes are all shown in yellow – were you right? 1 4 3 2 5 7 8 6

5. What makes a pair of shapes “congruent”?
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What makes a pair of shapes “congruent”?
Same angles
Same side lengths
Can be rotated or a mirror image
A cut-out of one shape will always fit exactly over the other
Click the green box if you want to go back to the first “congruent shapes” question page.
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6. 2. Which of these shapes are congruent to the yellow one?
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2. Which of these shapes are congruent to the yellow one? 1 4 2 3 8 5 6 9 7
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7. Congruent shapes are all shown in yellow – were you right?
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Congruent shapes are all shown in yellow – were you right? 4 1 2 3 8 6 5 9 7

8. Similar shapes

9. Which of these shapes are similar to the yellow one?
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Which of these shapes are similar to the yellow one? 1 4 3 2 5 7 8 6
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10. Similar shapes are all shown in yellow – were you right?
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Similar shapes are all shown in yellow – were you right? 1 4 3 2 5 7 8 6

11. What makes a pair of shapes “similar”?
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What makes a pair of shapes “similar”?
Same angles
Sides in the same proportion
Can be rotated or reflected
One is an enlargement of the other
Scale factor gives degree of enlargement:
Scale factor 2 → size is doubled
Scale factor 0.5 → size is halved
Scale factor 1 → size doesn’t change → congruent too
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12. Start page
Using similarity
Since shapes are similar, their sides are in the same proportion
=> = a
9cm
12cm
Multiply both sides by 12
=> 12 x 6 = a 9
6cm
=> a = 12 x 2 = 4 x 2 a
=> a = 8cm

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Which of these shapes are similar to the yellow one? (They aren’t drawn to scale) 1 2 12 3 8 9 9 18 4 4 5 6 6 6 12 9 4
4.5 6 3
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14. Similar shapes are shown in yellow – were you right?
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Similar shapes are shown in yellow – were you right? 1 9 12 2 4 8 3 12 18 9 4 6 5 6 9 6 6
4.5 3

15. Scale factor = new value old value.
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Scale factor = new value old value.
Scale factor?
New value =
Old value
12 = 3 or 1.5
8cm
12cm
Scale factor?
5cm
New value =
Old value
8 = 2
7.5cm
Can you see the relationship between the two scale factors?

16. Using scale factor Enlarge with scale factor 3 a = 9 x 3 = 27cm 9cm a
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Using scale factor
Enlarge with scale factor 3
a = 9 x 3 = 27cm
9cm a
What will the scale factor be? b
SF = new/old = 9/27 = ⅓
OR reciprocal of 3 = ⅓
15cm
b = 15 x ⅓ = 15 ÷ 3 = 5cm

17. Similar shapes - summaryb c x y z
Ratio a:b:c = ratio x:y:z
So: a = x a = x b = y
b y c z c z
To see whether 2 shapes are similar, put each ratio in its simplest form and see if they match.
Scale factor = new measurement
old measurement SF
new
old
Old measurement x SF = new measurement
- Scale factor more than 1 => shape gets bigger
Scale factor less than 1 => shape gets smaller
Congruent shapes are similar shapes with SF = 1
Remember: only side lengths change; angles stay the same!