Section 2.4 Duplicating an Angle
¶It's easy to use a compass to duplicate a line segment; that's what it's designed to do. But how does one duplicate an angle with straightedge and compass?
As shown in Figure 2.4.1, the goal is to duplicate \(\angle ABC\) with given side \(DE\text{.}\) Start by drawing an arbitrary circle at \(B\text{,}\) then duplicating it at \(E\text{,}\) marking all intersection points with the given line segments. Now use a compass to draw a circle centered at the intersection point on \(DE\) whose radius matches the distance between the intersection points on \(AB\) and \(BC\text{.}\) Intersect the circles and connect the dots with a straightedge, and \(\angle ABC\) has been duplicated as \(\angle DEF\text{.}\)