This page contains a geoboard environment that can be used for
circle work as well as well as other problems (such as Pick's
). There are also a number of problems that introduce
circle theorems, all of which have a special version of the
interactivity to support them. By working on the problems learners
will develop a better understanding of some of the angle properties
A generic environment for supporting work on geometry and area can
be found here
offers a good preparation for the problems Subtended
which lead towards the circle theorems.
Students will only need to know that the angles round a point add
up to 360° and how to calculate angles in isosceles
"How many different triangles can
you make which consist of the centre point and two of the points on
the edge? Can you work out each of their angles?"
"What is the relationship between
the angle at the centre and the angles at the circumference, for
angles which stand on the same arc? Can you prove it?
focusses on the angle subtended by a semicircle.
"Can you make a right-angled
triangle on this peg-board by joining up three points round the
edge?What do you notice and can you explain it?"
"Make five different
quadrilaterals on a nine-point pegboard, without using the centre
peg. Work out the angles in each quadrilateral you make. Now, what
other relationships you can see?"