Similar

In Geometry, two shapes are Similar if the only difference is size (and possibly the need to turn or flip one around).

Resizing is the Key

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!

There may be Turns, Flips or Slides, Too!

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.

Rotation		Turn!
Reflection		Flip!
Translation		Slide!

Examples

These shapes are all Similar:

Resized	Resized and Reflected	Resized and Rotated

Why is it Useful?

When two shapes are similar, then:

• corresponding angles are equal, and
• the lines are in proportion.

	Example: What is the missing length here?
	Notice that the red triangle has the same angles as the main triangle ... ... they both have one right angle, and a shared angle in the left corner
	In fact you could flip over the red triangle, rotate it a little, then resize it and it would fit exactly on top of the main triangle. So they are similar triangles. So the line lengths will be in proportion, and we can calculate: ? = 80 × (130/127) = 81.9 (No fancy calculations, just common sense!)

Congruent or Similar?

If you don't need to resize to make the shapes the same, they could really be Congruent. So, if the shapes become the same:

If you ...		Then the shapes are ...
... only Rotate, Reflect and/or Translate		Congruent
... need to Resize		Similar