Congruence (geometry): Difference between revisions
Content deleted Content added
No edit summary |
No edit summary |
||
| Line 3: | Line 3: | ||
Two sets that are not congruent are called ''non-congruent''. |
Two sets that are not congruent are called ''non-congruent''. |
||
For instance: |
|||
* * * |
|||
* * * * * |
|||
***** ***** *** *** |
|||
* * * |
|||
* * |
|||
The first two figures are congruent to each other. The third is a different size, and so is [[similar]] but not congruent to the others; the fourth is different altogether. Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like [[distance|distances]] and [[angle|angles]]. The latter sort of properties are called [[invariants]] and studying them is the essence of geometry. |
|||
Revision as of 19:00, 16 February 2002
Two sets in Rn (and especially two shapes in R2) are called congruent if one can be mapped onto the other by a combination of a translation, rotation and reflection.
Two sets that are not congruent are called non-congruent.
For instance:
* * * * * * * * ***** ***** *** *** * * * * *
The first two figures are congruent to each other. The third is a different size, and so is similar but not congruent to the others; the fourth is different altogether. Note that congruences alter some properties, such as location and orientation, but leave others unchanged, like distances and angles. The latter sort of properties are called invariants and studying them is the essence of geometry.