Tips on attempting Geometrical Proof questions (O Levels E Maths/A Maths)
1) Draw extended lines and additional lines. (using pencil)
Drawing extended lines, especially parallel lines, will enable you to see alternate angles much easier (look for the “Z” shape). Also, some of the more challenging questions can only be solved if you draw an extra line.
2) Use pencil to draw lines, not pen
Many students draw lines with pen on the diagram. If there is any error, it will be hard to remove it.
3) Rotate the page.
Sometimes, rotating the page around will give you a fresh impression of the question. This may help you “see” the way to answer the question.
4) Do not assume angles are right angles, or lines are straight, or lines are parallel unless the question says so, or you have proved it.
For a rigorous proof, we are not allowed to assume anything unless the question explicitly says so. Often, exam setters may set a trap regarding this, making the angle look like a right angle when it is not.
5) Look at the marks of the question
If it is a 1 mark question, look for a short way to solve the problem. If the method is too long, you may be on the wrong track.
6) Be familiar with the basic theorems
The basic theorems are your tools to solve the question! Being familiar with them will help you a lot in solving the problems.
Hope it helps! And all the best for your journey in learning Geometry! Hope you have fun.
“There is no royal road to Geometry.” – Euclid