Two shapes are Similar when the only difference is size (and possibly the need to turn or flip one around).
If one shape can become another using Resizing (also called dilation, contraction, compression, enlargement or even expansion), then the shapes are Similar:
|These Shapes are Similar!|
Sometimes it can be hard to see if two shapes are Similar, because you may need to turn, flip or slide one shape as well as resizing it.
These pairs of shapes are all Similar:
|Resized||Resized and Reflected||Resized and Rotated|
When two shapes are similar, then:
This can make life a lot easier when solving geometry puzzles, as in this example:
Shapes are Congruent when they are the same size (but may have been rotated, reflected or moved). So when the shapes become the same:
|When we ...||Then the shapes are ...|
|... only Rotate, Reflect and/or Translate||
|... also need to Resize||
Most people (including us) say "Congruent shapes are also Similar".