Which type of triangle will always have a perpendicular bisector that is also an angle bisector?

In an equilateral triangle, all three sides and angles are equal. The line from a vertex to the midpoint of the opposite side is both perpendicular to that side and bisects the vertex angle, so it is both a perpendicular bisector and an angle bisector. The other triangle types do not always have this property.

AI-written and checked against the verified answer.