Editing Symmedian (section)

==Isogonality==
Many times in geometry, if we take three special lines through the vertices of a triangle, or ''[[cevian]]s'', then their reflections about the corresponding angle bisectors, called ''isogonal lines'', will also have interesting properties. For instance, if three cevians of a triangle intersect at a point {{mvar|P}}, then their isogonal lines also intersect at a point, called the [[isogonal conjugate]] of {{mvar|P}}.

The symmedians illustrate this fact. 
* In the diagram, the medians (in black) intersect at the [[centroid]] {{mvar|G}}.
* Because the symmedians (in red) are isogonal to the medians, the symmedians also intersect at a single point, {{mvar|L}}. 
This point is called the triangle's '''symmedian point''', or alternatively the '''Lemoine point''' or '''Grebe point'''.

The dotted lines are the angle bisectors; the symmedians and medians are symmetric about the angle bisectors (hence the name "symmedian.")