is constructing a perpendicular bisector similar to constructing an angle bisector both constructions begin with a given angle

Answer 1

No, constructing a perpendicular bisector and constructing an angle bisector are different constructions.

Constructing a perpendicular bisector involves finding the line or segment that bisects another line segment at a right angle (90 degrees). This is done by finding the midpoint of the line segment and then constructing a line or segment perpendicular to it.

Constructing an angle bisector involves finding the line or segment that divides an angle into two equal parts. This is done by constructing an arc from each side of the angle, and then finding the point where the intersecting arcs meet. This point will be equidistant from each side of the angle and will bisect the angle.