What are similar shapes? Real life examples on similar shapes.

Two shapes are said to be similar if the all the sides of both shapes have been enlarged by the same scale factor. So all you need to do is work out the scale factors for the corresponding sides and if they are equal then the two shapes will be similar. Let’s take a look at a few examples:

Example 1

A small picture frame has a length of 5 inches and a height of 3 inches. A larger picture frame has length of 15 inches and a height of 9 inches. Prove that the two picture frames are similar shapes.


Length scale factor:

15 ÷ 5 = 3

Height scale factor:

9 ÷ 3 = 3

So the two picture frames are similar as both lengths have the same scale factor.

Example 2

A small window has a base length of 0.5m and a height of 0.75m. A larger window has a base length of 1.2m and a height of 1.5m. Are the two windows similar shapes?

Base length scale factor:

1.2 ÷ 05 = 2.4

Height scale factor:

1.5 ÷ 0.75 = 2

Since the scale factors are different then the two windows are not similar shapes.

Example 3

A bank note has a length of 140mm and a width of 50mm. A slightly larger bank note has a length of 182mm and a width of 65mm. Are the two bank notes similar rectangles.

Length scale factor:

182 ÷ 140 = 1.3

Width scale factor:

65 ÷ 50 = 1.3

Since the bank notes have been enlarged by the same scale factor then the two bank notes are similar shapes.

For some easier similar shape questions click here.

For some similar triangle questions click here.

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