Similar Triangle Help. How to Identify Similar Triangles (Shapes)

In this article you will be able to identify if two triangles are mathematically similar.

To prove that two triangles are similar work out the scale factors for all 3 sides of the triangle. Do this by diving each pair of matching sides. If all the scale factors are equal for all 3 sides of the triangles then the two triangles will be similar.

Example 1

Prove that these two right angled triangles are similar shapes.

All you need to do is work out the scale factors of the 3 lengths of the triangle.

Base Scale Factor:

32 ÷ 8 = 4

Height Scale Factor:

24 ÷ 6 = 4

Slanted Length Scale Factor:

40 ÷ 10 = 4

Since all the scale factors are the same then the two triangles are similar.

Example 2

Are these two triangles are similar?

All you need to do is work out the scale factors of the 3 lengths of the triangle.

Scale factor of edge 1:

6 ÷ 2 = 3

Scale factor of edge 2:

21 ÷ 7 = 3

Now the two sides so far have the same scale factor, but the third side needs to have the same factor as well if the two shapes are going to be similar.

36 ÷ 9 = 4

The bottom edge has a scale factor of 4 which is different from the other two sides. Therefore the two triangle are not similar as the scale factors are not all the same.

Try these links below on similar shapes for more help:

Similar shapes

Real life similar shapes

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