1. [ GM3.1 Extension Starter]
Construction
[ GM3.1 Extension Starter]
Draw one or more of these – think before you start!
A regular 12-sided polygon.
b) A square.
A rhombus with two internal angles of 60°.
d) A pair of parallel lines. There may be several different ways – be prepared to explain your method!
e) Why must the opposite sides of a regular octagon be parallel to each other?
Preamble
These constructions (and their explanations) suit pupils working individually or in pairs.
Possible content
Using standard construction methods.
Resources
Compasses and rulers.
Solution/Notes
a) 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.
e) Considering the congruent triangles making the octagon these two faces must be parallel using alternate angles.
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010