Symmedian
![A triangle with medians (blue), angle bisectors (green) and symmedians (red). The symmedians intersect in the symmedian point K, the angle bisectors in the incenter I and the medians in the centroid G.](/Images/godic/202502/14/Symmedians2027.png")
In geometry, symmedians are three particular geometrical lines associated with every triangle. They are constructed by taking a median of the triangle (a line connecting a vertex with the midpoint of the opposite side), and reflecting the line over the corresponding angle bisector (the line through the same vertex that divides the angle there in half). The angle formed by the symmedian and the angle bisector has the same measure as the angle between the median and the angle bisector, but it is on the other side of the angle bisector.