The reflection of a line through a vertex in the bisector of the angle at that vertex is called its isogonal line. Thus AX and AY are isogonals if BAX = CAY or BAY = CAX.
The isogonals of three concurrent lines are themselves concurrent. These pairs of points are called isogonal conjugates of each other.
1. The medians meet at the midcentre or centroid. The centroid is the centre of mass of a uniform triangular region.
2. The bisectors of the angles meet at the incentre. Related points are the Gergonne centre and Nagel centre and the three "excentres".
3. The Morley centre is the centre of the regular triangle of points formed by pairs of angle trisectors.
4. The Symmedian or Lemoine Centre is the point where the isogonals of the medians (the symmedians) meet, G'. (the isogonal conjugate of the centroid G).
5. The Fermat Centre is where lines from the vertices form a star (that is the angles between them are all 60°).