MEI Maths Item of the Month
November 2015
Three Line Whip
Construct an equilateral triangle with one vertex on each of 3 parallel lines using just a
straight edge and a pair of compasses.
Solution
Add a point on the middle line and use a compass with a fixed width to create a line at 60° to
the parallel lines at this point.
Construct a line parallel to this with the same distance between them as the bottom two
lines: find the point of intersection of this line with the bottom line, construct a circle through
this point with centre on the original point, find the intersections of this circle with the bottom
two lines and draw a line through these.
1 of 2
TB v1.0 © MEI
31/03/2016
MEI Maths Item of the Month
Find the intersection of this line with the top line and then draw a circle with a centre on the
original point that passes through this point. Find the intersection of this circle with the
bottom line (on the same side as the top point).
2 of 2
TB v1.0 © MEI
31/03/2016