# Bisector via angles (isosceles triangle)

- Author:
- Zoltán Kovács

- Topic:
- Angles, Isosceles Triangles

`LocusEquation[AreCongruent[α,β],C]`

determines where to put *C*in order to the angles

*α*and

*β*are equal. With no doubt

*C*must take place on the bisector of

*AB*. In such cases the triangle will be isosceles. There is, however, one remarkable issue. GeoGebra draws not only the bisector of

*AB*, but also

*AB*, as the final result. The reason is that instead of computing

*α*=

*β*, cos(

*α*)=cos(

*β*) is used. This problem has its roots in complex algebraic geometry, and currently cannot be handled elegantly in GeoGebra.

## Notes

- This is a "heavy" applet. Currently (as of July 2016) it requires too much resources to run in the web version of GeoGebra. You may encounter problems when dragging the points.
- The same effect should be performed by entering
`LocusEquation[α==β,C]`

, but this kind of easier input syntax (as of July 2016) is not yet supported.