Constructions Draw one or more of these – think before you start! [GM3.1 Core Plenary] Draw one or more of these – think before you start! A regular 12-sided polygon. A square. A rhombus with two internal angles of 60°. A pair of parallel lines. There may be several different ways – be prepared to explain your method! Preamble Some challenging tasks that give pupils the opportunity to think in greater depth about these common constructions and apply them. The whole-group post-task discussion is important. The task is suitable for pairs or small groups. Possible content Using and applying standard constructions. Resources Compasses and rulers. Solution/Notes Construct a hexagon in the normal way then bisect the sides, producing the bisector to the circle. Joining these points together with the vertices of the hexagon gives a regular 12-sided polygon. By constructing four right-angles and equal sides using compasses. Construct a 60° angle then two equal arcs define the adjacent vertices with the fourth vertex being found by using the same radii from these. There are several approaches involving circles or constructing lines making equal angles to a third line. Original Material © Cambridge University Press 2010 Original Material © Cambridge University Press 2010