Question

How is constructing a perpendicular bisector similar to constructing an angle bisector? How is it different?

Answer 1

Similarity: you must use equidistant overlapping arcs, from set points that are equidistant from the center, to create the bisector.
Difference: a perpendicular bisector requires two overlapping arcs, one on each side of the segment, while the angle bisector only requires one overlapping arc - the other point for the angle bisector is the vertex.