Please explain: How can I tell whether two copies are scaled figures or not, if both shapes look similar and a smaller shape is inside a bigger shape?

Question

Please explain: How can I tell whether two copies are scaled figures or not, if both shapes look similar and a smaller shape is inside a bigger shape?

Answer 1

Take the ratios of the corresponding sides of the two shapes.  If the ratios are consistent, then they are proportional.  This means that the corresponding sides of the shapes have a common scale factor.  Thus, they are similar.

 

For example, it the consistent ratio of the figures is 2, then the corresponding sides have a common scale factor of 2.