Interior-angle bisector at a vertex as an InfiniteLine
AngleBisector[{q1, p, q2}]
AngleBisector[{q1, p, q2}, "type"]
bisector = AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}]
→ InfiniteLine[{0, 0}, {3/2, Sqrt[3]/2}]AngleBisector[{{1, 0}, {0, 0}, {1, Sqrt[3]}}]
→ InfiniteLine[{0, 0}, {3/2, Sqrt[3]/2}]AngleBisector[{{1, 0}, {0, 0}, {Sqrt[3], 1}}]
→ InfiniteLine[{0, 0}, {(2 + Sqrt[3])/2, 1/2}]