Let's compare the ratios for the lengths of the sides of Square A and Square B for each of the following diagrams.

Square A to Square B
Square A : Square B
1 unit : 3 units (for each corresponding side)
Square A to Square B
Square A : Square B
1 unit : 4 units (for each corresponding side)

You might have noticed the following:

  • The ratios of the corresponding side lengths of the similar shapes are equal. As such, this relationship can be represented by a single ratio.
  • The ratio of the side lengths of two similar shapes is called the scale factor.

Example 1

Which triangles are similar? Explain.

Compare the ratios of the corresponding sides.

\(\triangle\)C : \(\triangle\)D \(\triangle\)C : \(\triangle\)E \(\triangle\)D : \(\triangle\)E
\(\triangle\)C is not similar to \(\triangle\)D \(\triangle\)C is similar to \(\triangle\)E \(\triangle\)D is not similar to \(\triangle\)E

Triangles C and E are similar because the ratios of the lengths of corresponding sides (the scale factors of the sides) are the same.