Yes - the altitude of an equilateral triangle is perpendicular to the side chosen as the base and bisects that side and the opposite angle.
Also, the altitude of an isosceles triangle when measured from the third side (the side that is not equal to the other two sides) is a perpendicular bisector of the base and also bisects the opposite angle.
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Biconditional Statement for: Perpendicular Bisector Theorem: A point is equidistant if and only if the point is on the perpendicular bisector of a segment. Converse of the Perpendicular Bisector Theorem: A point is on the perpendicular bisector of the segment if and only if the point is equidistant from the endpoints of a segment.
The Perpendicular bisector concurrency conjecture is the circumcenter
The perpendicular bisector of a line segment AB is the straight line perpendicular to AB through the midpoint of AB.
Equilateral triangles
Perpendicular Bisector