Constructions and Tilings — Question 5

Let ∠XOY be the given angle. Fix a small pole at the point O. Take a rope and make a loop at one end. Mark a point at some distance on the rope. Fix the loop of the rope at the pole at O and rotate the rope from OX to OY. Mark points A and B at a fixed distance mark on the rope. Fix small poles at A and B. Take a rope and make loops on both ends. Fix the loops of this piece of rope with poles at A and B. Mark the midpoint of this rope and hold the rope at the midpoint. Make both ends of the rope tight and mark the point at the midpoint of the rope. Let this point be M. Join AM, BM, and OM. We have OA = OB and AM = BM. In ∆OAM and ∆OBM, we have OA = OB, AM = BM, and OM is common. ∴ ∆OAM = ∆OBM (Using SSS-rule) ∴ ∠AOM = ∠BOM ∴ ∠XOM = ∠YOM ∴ OM is the bisector of the given angle ∠XOY.