Definition:Similar Figures
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Definition
Two rectilineal figures are similar iff:
- 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.
It is appreciated that this definition is circular. This will be addressed once Algebraic Geometry has been tackled properly.
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Euclid's Definition
As Euclid defined it:
- Similar rectilineal figures are such as have their angles severally equal and the sides about the equal angles proportional.
