median
don steward
mathematics teaching 10 ~ 16

## Thursday, 1 December 2011

### constructions

initial compass practice can be helpful for some students

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

Patrick Honner's blog contains the suggestion that students can create the angle bisectors (and so the incentre) by paper folding:

and the line bisectors
to construct the circumcentre

to practice the (bisector) constructions using compasses and a straight edge, students can be asked to construct all three angle bisectors of a triangle

with sufficient accuracy the lines will meet at a point, the 'incentre', and this circle can be drawn:

also for the perpendicular bisectors of the sides of a triangle - creating the 'circumcentre'

this probably needs a sheet of plain paper
possibly informing students that they can vary their compass radius for each side bisection

sometimes this circumcentre lies:
• inside the triangle
• outside it
• (borderline case) 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 (i.e. the circumcircle):

explore how three points determine a circle

usually...
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

how to construct a parallel to a line (CD) through a given point (A) :