# Regular pentagon erected internally on a side of a regular decagon

- Author:
- Zoltán Kovács

Regular pentagon

*ABKLM*is erected internally on the side*AB*of a regular decagon*ABCDEFGHIJ*. Now vertex*L*of the pentagon is the midpoint of the decagon. Since version 5.0.393.0 GeoGebra is able to check this property symbolically as well. Just click on the Relation tool and select segments*b*and then*c*, and finally choose "More...".## Activity

Check some other equalities concerning other segments in the decagon (or the pentagon) by joining some vertices and comparing the appearing segments with the Relation tool.

## Theorems that are true on parts

Segments

*b*and*c*are equal in fact just on parts. The reason behind this is that GeoGebra cannot distinguish between regular polygons and star-regular polygons. It considers all cases at the same time. Note that there is a star-regular pentagon, {5/2}, and there is also a star-regular decagon, namely {10/3}, as well. That is, all statements on the given construction here is considered on 2x2=4 different setups in the background! Also, the segments BK and CD are parallel just on parts. A similar statement is true for segments KL and EF, too, for instance.