3. 1. Which of these shapes are1. Which of these shapes are
congruentcongruent to theto the yellowyellow one?one?
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5
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1
7
6
8
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4. CongruentCongruent shapes are all shown inshapes are all shown in
yellowyellow – were you right?– were you right?
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5. What makes a pair of shapesWhat makes a pair of shapes
““congruentcongruent”?”?
Same anglesSame angles
Same side lengthsSame side lengths
Can be rotated or a mirror imageCan be rotated or a mirror image
A cut-out of one shape will always fitA cut-out of one shape will always fit
exactly over the otherexactly over the other
Click the green box if you want to go back toClick the green box if you want to go back to
the first “congruent shapes” question page.the first “congruent shapes” question page.
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6. 2. Which of these shapes are2. Which of these shapes are
congruentcongruent to theto the yellowyellow one?one?
Answers
Start page
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5
1
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8
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7. CongruentCongruent shapes are all shown inshapes are all shown in
yellowyellow – were you right?– were you right?
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9. Which of these shapes areWhich of these shapes are similarsimilar
to theto the yellowyellow one?one?
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10. SimilarSimilar shapes are all shown inshapes are all shown in
yellowyellow – were you right?– were you right?
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1
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11. What makes a pair of shapesWhat makes a pair of shapes
““similarsimilar”?”?
Same anglesSame angles
Sides in the same proportionSides in the same proportion
Can be rotated or reflectedCan be rotated or reflected
One is an enlargement of the otherOne is an enlargement of the other
Scale factor gives degree of enlargement:Scale factor gives degree of enlargement:
– Scale factor 2Scale factor 2 →→ size is doubledsize is doubled
– Scale factor 0.5Scale factor 0.5 →→ size is halvedsize is halved
– Scale factor 1Scale factor 1 →→ size doesn’t changesize doesn’t change →→ congruent toocongruent too
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“similar shapes” question page.“similar shapes” question page.
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12. Using similarityUsing similarity
9cm 12cm
6cm
a
Since shapes are similar, their
sides are in the same proportion
Multiply both sides by 12
=> 12 x 6 = a
9
=> a = 12 x 2 = 4 x 2
3 1
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=> 6 = a
9 12
=> a = 8cm
13. Which of these shapes areWhich of these shapes are similarsimilar
to theto the yellowyellow one?one?
(They aren’t drawn to scale)(They aren’t drawn to scale)
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9
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9
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4.5
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12
18
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14. SimilarSimilar shapes are shown inshapes are shown in yellowyellow
– were you right?– were you right?
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15. Scale factor =Scale factor = new valuenew value
old valueold value..
8cm 12cm
Scale factor?
Scale factor?
5cm
7.5cm
New value =
Old value
New value =
Old value
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12 = 3 or 1.5
8 2
Can you see the relationship between the two scale factors?
8 = 2
12 3
16. Using scale factorUsing scale factor
9cm a
Enlarge with
scale factor 3
b
15cm
a = 9 x 3 = 27cm
SF = new/old = 9/27 = ⅓
What will the
scale factor be?
b = 15 x ⅓ = 15 ÷ 3 = 5cm
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OR reciprocal of 3 = ⅓
17. Similar shapes - summarySimilar shapes - summary
a
b
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
- Scale factor more than 1 => shape gets bigger
- Scale factor less than 1 => shape gets smaller
- Congruent shapes are similar shapes with SF = 1
Old measurement x SF = new measurement
Remember: only side lengths change; angles stay the same!
SF
new
old
