Approaching a geometric problem
The following list of suggestions has been useful in assisting students who have difficulty starting geometry problems.
- First read any text and examine the diagram.
- Update the diagram to include all information from the text.
Look for a clue as to how or where to start.
(e.g. By considering ΔABC…; Show that…; Using similar triangles…)
Examine key geometrical features that are indicated.
(e.g. parallel lines, equal angles, given measurements)
- Use colour to highlight any shapes mentioned specifically in the question. Use a different colour for each shape. You can download the Looking beyond the lines slide presentation to see an example.
Sometimes seeing the diagram from a new perspective will help. Reorient the diagram by turning the page around or draw the diagram in a different order.
Are there any auxiliary lines that could be added to the diagram?
(e.g. produce a line segment or construct parallel lines through given points)
Can properties of polygons be used?
(e.g. triangle and quadrilateral properties, congruence, similarity)
- If the problem is about angles, introduce pronumerals to label them. Work through the diagram indicating relationships in terms of the introduced pronumerals (or given values).
You can download the Great angle chase slide presentation which shows one solution to a very complex angle problem.
Frequently students may have a conceptual understanding of the solution before they have developed the ability to communicate that understanding in the formal language required in a proof.