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- They have corresponding angles, all of which are equal
- They have corresponding sides, all of which are proportional.
It is intuitively understood what it means for two figures to have the same shape.
In the words of Euclid:
- Similar rectilineal figures are such as have their angles severally equal and the sides about the equal angles proportional.
This is still in use and can still be seen, but is not universal.
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Entry: similar (of figures)