1. Construction and congruence
[ GM3.1 Extension Plenary]
You should be able to do these tasks using compasses and rulers only:
construct a regular hexagon
construct an equilateral triangle
copy an angle
construct the perpendicular bisector of a straight line
construct the line bisecting an angle
construct a perpendicular line from a point to another line.
Pick one or more of the above and use what you know about congruent triangles to show why they work.
Preamble
These tasks are suited to small group work with each group reporting to the larger group – perhaps in the form of a mini-presentation. Very often pupils are not fully aware of the geometry behind constructions but this knowledge can certainly aid their retention. The field of proof – in general terms – may be touched upon.
Possible content
Using congruency to explain the veracity of some standard constructions.
Resources
Preferably none but possibly compasses and rulers if a more concrete approach is adopted.
Solution/Notes
Pupils’ own explanations of standard compass and ruler constructions based on congruent triangles – do not expect (or aim for) rigorous geometric proofs.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010