HARDER 3 UNIT - CIRCLE GEOMETRY
TIPS:
1. Do not be intimidated by the diagram. Take a minute to label your diagram with any equal angles or sides. These might help you later and may be harder to see once you have read all the additional information in the question.
2. If asked to redraw a diagram:
a) Make sure your diagram is as large as you can make it if the diagram is easy to draw.
b) For complicated diagrams trace the diagram very carefully drawn. Check points of intersection.
c) Your diagram should reflect your solution 100%. Every written line of your solution MUST be labelled on your diagram.
3. If you have several equal angles on the one diagram use algebra and let all the equal angles be x or y (but not the same letter as one of the vertices in the diagram). Introduce as few variables as possible into your solution.
4. A highlighter will be essential for all circle geometry questions. A fine point (rather than thick) highlighter will prevent your diagram from becoming too complicated. Readily use your highlighter to outline, for example, similar triangles, equal angles, parallel lines, cyclic quadrilaterals etc. Highlight important relationships you may need to use later in a question or if asked to show an expression eg. AB . EF = FA . BE then high light these expressions (or part thereof) when they appear in your working.
5. If asked to show something try to work backwards. Look at what you have to show, identify this on your diagram and think about how you can get there.
6. If you need to prove similar triangles do not forget to redraw each triangle separately on your paper with the corresponding angles lined up. Also write down the proportion statement for the triangles. It may be helpful.
7. The word deduce will indicate you can use a relationship you have previously proven.
8. Look for opportunities where you can use the word similarly. If you repeat the same theorem for two consecutive lines of working do not write it twice, use similarly.
9. If you can’t answer part of a question make sure you label the information you gain from that part onto your diagram and move to the next part. Your diagram should be clearly labelled with all the given information. Use different colours to label different information if it will help.
10. Once you have figured out how to answer the question, number your diagram in pencil in the order in which you will write out the proof. This does not take long and will give you clarity as to how to put your answer together.
11. Be particular with your setting out:
∠ BAC = ____ (..................reason...................)
For nearly every line of working you will need to provide a reason. Sometimes you can group lines together using one theorem BUT be careful not to leave out important reasoning. Your proof should read like a novel.
1. Do not be intimidated by the diagram. Take a minute to label your diagram with any equal angles or sides. These might help you later and may be harder to see once you have read all the additional information in the question.
2. If asked to redraw a diagram:
a) Make sure your diagram is as large as you can make it if the diagram is easy to draw.
b) For complicated diagrams trace the diagram very carefully drawn. Check points of intersection.
c) Your diagram should reflect your solution 100%. Every written line of your solution MUST be labelled on your diagram.
3. If you have several equal angles on the one diagram use algebra and let all the equal angles be x or y (but not the same letter as one of the vertices in the diagram). Introduce as few variables as possible into your solution.
4. A highlighter will be essential for all circle geometry questions. A fine point (rather than thick) highlighter will prevent your diagram from becoming too complicated. Readily use your highlighter to outline, for example, similar triangles, equal angles, parallel lines, cyclic quadrilaterals etc. Highlight important relationships you may need to use later in a question or if asked to show an expression eg. AB . EF = FA . BE then high light these expressions (or part thereof) when they appear in your working.
5. If asked to show something try to work backwards. Look at what you have to show, identify this on your diagram and think about how you can get there.
6. If you need to prove similar triangles do not forget to redraw each triangle separately on your paper with the corresponding angles lined up. Also write down the proportion statement for the triangles. It may be helpful.
7. The word deduce will indicate you can use a relationship you have previously proven.
8. Look for opportunities where you can use the word similarly. If you repeat the same theorem for two consecutive lines of working do not write it twice, use similarly.
9. If you can’t answer part of a question make sure you label the information you gain from that part onto your diagram and move to the next part. Your diagram should be clearly labelled with all the given information. Use different colours to label different information if it will help.
10. Once you have figured out how to answer the question, number your diagram in pencil in the order in which you will write out the proof. This does not take long and will give you clarity as to how to put your answer together.
11. Be particular with your setting out:
∠ BAC = ____ (..................reason...................)
For nearly every line of working you will need to provide a reason. Sometimes you can group lines together using one theorem BUT be careful not to leave out important reasoning. Your proof should read like a novel.