AQA · Mathematics · 8300
GCSE Maths: Similar shapes: finding sides
Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths practice questions for Similar shapes: finding sides (Corbettmaths Video 292), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.
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What does it mean for two shapes to be similar?
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Two shapes are similar when their corresponding angles are equal and their corresponding sides are in the same ratio (proportional).
How do you find a missing side length in a pair of similar shapes?
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Find the scale factor by dividing corresponding known sides, then multiply (or divide) another known side by that scale factor to find the missing length.
In similar shapes, corresponding sides are in the same ?.
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ratio
If rectangle ABCD is similar to rectangle EFGH with sides in ratio 2:5, and AB = 6 cm, what is EF?
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15 cm. The scale factor is 5/2, so EF = 6 × (5/2) = 15 cm.
Why are two rectangles with sides 4 cm by 6 cm and 6 cm by 8 cm NOT similar?
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The ratios of corresponding sides are not equal: 4/6 ≠ 6/8 (or 2/3 ≠ 3/4), so they are not similar.
Why is it incorrect to say two triangles are similar just because the same length has been added to both the height and base?
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Adding the same length does not preserve the ratio between sides. Similar shapes require sides to be in the same ratio (multiplied by a scale factor), not increased by the same additive amount.
If two similar rectangles have a length scale factor of 3, what is the area scale factor?
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9. The area scale factor is the square of the length scale factor: 3² = 9.
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