Beyond the compass: Exploring geometric constructions via a circle arc template and a straightedge

Figure 1.  Compass constructions made easy [11]

Figure 2.  Circle arc template

Figure 3.  A given line segment $ \overline {AB} $

Figure 4.  Circle arc template with centre at $ A $

Figure 5.  Circle arc template with centre at $ A $

Figure 6.  A first arc

Figure 7.  Circle arc template with centre at $ B $

Figure 8.  Second arc with intersection points labelled

Figure 9.  Intersection points, $ D $ and $ E $

Figure 10.  Straightedge aligned with points $ D $ and $ E $

Figure 11.  Line segment $ \overline {DE} $ constructed

Figure 12.  Finished construction. $ \overline {DE} $ is the perpendicular bisector of $ \overline {AB} $

Figure 13.  Line segment $ \overline {AB} $

Figure 14.  Circle arc template with centre at $ A $

Figure 15.  Marking point of intersection made with $ \overline {AB} $

Figure 16.  Point of intersection labelled $ P $

Figure 17.  Circle arc template with centre at $ B $

Figure 18.  Marking point of intersection made with $ \overline {AB} $

Figure 19.  Point of intersection labelled $ S $

Figure 20.  Circle arc template with centre at $ P $

Figure 21.  Marking point of intersection made with $ \overline {AB} $

Figure 22.  Point of intersection labelled $ Q $

Figure 23.  Circle arc template with centre at $ S $

Figure 24.  Marking point of intersection made with $ \overline {AB} $

Figure 25.  New point of intersection labelled $ R $

Figure 26.  Circle arc template with centre at $ Q $

Figure 27.  Arc with centre at point $ Q $

Figure 28.  Circle arc template with centre at $ R $

Figure 29.  Arc with centre at point $ R $ and intersection points labelled

Figure 30.  Intersection points $ D $ and $ E $

Figure 31.  Straightedge aligned with points $ D $ and $ E $

Figure 32.  Straightedge aligned with points $ D $ and $ E $

Figure 33.  Finished construction. $ \overline {DE} $ is the perpendicular bisector of $ \overline {AB} $

Figure 34.  $ \angle AOB $

Figure 35.  Circle arc template with centre at $ O $

Figure 36.  Marking point of intersection, $ P $

Figure 37.  Marking point of intersection, $ Q $

Figure 38.  $ \angle AOB $ with points $ P $ and $ Q $

Figure 39.  Circle arc template with centre at $ P $

Figure 40.  'Small' section of arc traced, with centre at $ P $

Figure 41.  Circle arc template with centre at $ Q $

Figure 42.  Arc with centre at $ Q $ intersecting previous arc to form point $ C $

Figure 43.  Line segment $ \overline {OC} $ is constructed using straightedge

Figure 44.  Finished construction. $ \overline {OC} $ is the bisector of $ \angle AOB $

Figure 45.  Line Segment $ \overline {AB} $ and point $ P $

Figure 46.  Circle arc template with centre at $ P $

Figure 47.  Points $ Q $ and $ R $ constructed

Figure 48.  Drawing arc with centre at point $ Q $

Figure 49.  Drawing arc with centre at point $ R $

Figure 50.  New point of intersection labelled $ S $

Figure 51.  Line segment $ \overline {PS} $ is constructed using straightedge

Figure 52.  Finished construction. $ \overline {PS} $ is perpendicular to $ \overline {AB} $