Definition:Similar Figures

From ProofWiki
Jump to navigation Jump to search


Two rectilineal figures are similar if and only if:

They have corresponding angles, all of which are equal
They have corresponding sides, all of which are proportional.

Informal Definition

Two geometric figures are similar if they have the same shape but not necessarily the same size.

It is intuitively understood what it means for two figures to have the same shape.

Algebraic Definition

Two geometric figures are similar if one can be transformed into the other by means of a similarity mapping.

Euclid's Definition

In the words of Euclid:

Similar rectilineal figures are such as have their angles severally equal and the sides about the equal angles proportional.

(The Elements: Book $\text{VI}$: Definition $1$)

Historical Note

The symbol introduced by Gottfried Wilhelm von Leibniz to denote geometric similarity was the tilde: $\sim$

This is still in use and can still be seen, but is not universal.