Similar Shapes

This lesson covers:

  1. What mathematically 'similar' shapes are
  2. How to use scale factors to find the lengths of missing sides on similar shapes

Which feature(s) must be identical for two shapes to be considered 'similar'?

Their shape

Their rotation

Their position

Their size

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You can normally tell whether two shapes are similar just by looking at them. To be sure though, what would you need to confirm?

That all of the sides are the same length

That all of the angles are the same size

That all of the sides are the same length, and all of the angles are the same size

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Comparison of two shapes to determine similarity

Are the above shapes similar?

No

Yes

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Two rectangles with angles 86 and 94 degrees, asking if the shapes are similar.

Are the above shapes similar?

No

Yes

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Two similar quadrilaterals labeled A and B with side lengths of 10mm and 15mm respectively.

 The two quadrilaterals above are similar. What is the scale factor from shape A to shape B?

1.5

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Two similar quadrilaterals labeled A and B with side lengths, showing a scale factor from shape A to shape B.

 The two quadrilaterals above are similar. What is the scale factor from shape A to shape B?

0.5

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Two similar quadrilaterals with side lengths 15 cm and 18 cm for quadrilateral A, and 45 cm and x for quadrilateral B.

 The two quadrilaterals above are similar. What length is side x?

54

cm

cm

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When discussing shapes, do the terms 'similar' and 'mathematically similar' mean the same thing?

Yes

No

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Two similar quadrilaterals with side lengths labelled. Quadrilateral A has sides of 36mm and 72mm, and Quadrilateral B has a side of 18mm with another side labelled y.

 The two quadrilaterals above are similar. What length is side y?

9

mm

mm

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