Circle Theorems

'Discover and generalise the theorems about angles in circles using dynamic geometry'

This activity focusses on the important difference between a particular case and the general case. Using dynamic geometry, the aim is to construct different situations with circles, measure the angles and examine what happens with those angles as the points move dynamically within the constraints given. What would the diagram on the left look like if you dragged point A all the way round to the bottom? Would it still be the same construction? These and more questions arise from this investigation and really help with both generalising and examining the limits of a generalisation.

Resources

You will need access to a dynamic geometry package such as Cabri Geometre, Geometer's Sketchpad or Geogebra for this investigation. The activity can be run from the  angles in circles worksheet. 

Example

Below is a quick screencast of 'the arrow head' being constructed and changing dynamically. What are the patterns? How do they change as the shape changes? (screencast has no sound)

Description

  • Ensure familiarity with the dynamic geometry package being used. This includes constructing segments and polygons within circles and marking and measuring angles.
  • Follow the instructions in the worksheet to create the various constructions given.
  • Play dynamically with the constructions to look for patterns.
  • Generalise about the phenomena noticed.
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