don steward
mathematics teaching 10 ~ 16

Thursday, 1 December 2011


initial compass practice can be helpful to some students

the website sciencevsmagic is a great resource: 40 construction tasks to attempt

I like the suggestion (on Mr Honner's blog) that students can helpfully create the bisectors by paper folding:

to practice the constructions using compasses and a straight edge, students can be asked to draw the angle bisectors of a triangle
if they are accurate the lines will meet at a point, the 'incentre' and this circle can be drawn (and possibly coloured in):

(see a post entitled 'loci' for an alternative method for constructing an angle bisector)

same for the perpendicular bisectors of the sides of a triangle - creating the 'circumcentre'
this needed a sheet of plain paper (to draw the circumcircle) and some of students needed to be told they could vary their compass radius for each side bisection

sometimes this centre lies outside the triangle and sometimes on one of the sides of a triangle:

students can explore these three cases - noting the special case where the lines meet on one of the sides of the triangle

students can also be asked to bisect two joined ('hinged') lines - to find the centre of a circle that passes through the three points A, B and C (still the circumcircle):

three points determine a circle...
further tasks, practicing these skills, could be to:
  • construct a regular hexagon
  • construct a 30 degree angle (and a 45 degree angle)
  • construct an equilateral triangle

  • construct a parallel to a line through a given point

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