Congruent and similar Congruent and similar shapesshapes

Congruent shapes

Similar shapes

Congruent shapesCongruent shapes

1. Which of these shapes are 1. Which of these shapes are congruentcongruent to the to the yellowyellow one? one?

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CongruentCongruent shapes are all shown in shapes are all shown in yellowyellow – were you right? – were you right?

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What makes a pair of shapes What 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 fit A 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 to Click 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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2. Which of these shapes are 2. Which of these shapes are congruentcongruent to the to the yellowyellow one? one?

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CongruentCongruent shapes are all shown in shapes are all shown in yellowyellow – were you right? – were you right?

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Similar shapesSimilar shapes

Which of these shapes are Which of these shapes are similarsimilar to the to the yellowyellow one? one?

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SimilarSimilar shapes are all shown in shapes are all shown in yellowyellow – were you right? – were you right?

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What makes a pair of shapes What makes a pair of shapes ““similarsimilar”?”?

Same anglesSame anglesSides in the same proportionSides in the same proportionCan be rotated or reflectedCan be rotated or reflectedOne is an enlargement of the otherOne is an enlargement of the otherScale factor gives degree of enlargement:Scale factor gives degree of enlargement:– Scale factor 2 Scale factor 2 →→ size is doubled size is doubled– Scale factor 0.5 Scale factor 0.5 →→ size is halved size is halved– Scale factor 1 Scale factor 1 →→ size doesn’t change size doesn’t change →→ congruent too congruent too

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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

Which of these shapes are Which of these shapes are similarsimilar to the to the yellowyellow one? one?

(They aren’t drawn to scale)(They aren’t drawn to scale)

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SimilarSimilar shapes are shown in shapes are shown in yellowyellow – were you right?– were you right?

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Scale factor = Scale factor = new valuenew value old value old 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 = 212 3

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

Similar shapes - summarySimilar shapes - summary

a

b

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y

z

Ratio a:b:c = ratio x:y:zSo: 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