Did you know how to prove Geometry problems?
1. There is no fixed path to proving Geometry problems. You have some theorems, with which you have to prove a particular problem.
a. Therefore, remember the theorem statements, not by blindly memorising them, but by understanding them. Because without understanding, you will not be able to use them elsewhere.
b. Imagine, you are in class X. You are expected to remember all the theorems that you have learnt in your lower classes as well as in class X. You do not know, which one you will be needing while proving a particular problem.
(Do not say ‘who remembers what is a linear pair or its property’ etc.)
2. Draw the figure correctly with a pencil. A scalene triangle should not look like a right triangle or a rectangle should not seem to be a square. The correct logic will come to your mind when you will be able to visualise the given conditions correctly.
a. If you draw a square instead of a rectangle, you may be tempted to take all the sides equal (because the figure says so) and you will go wrong.
b. Similarly, an angle bisector of a triangle should appear as an angle bisector, else while proving, you may forget the information that the line divides the angle into two equal parts and may not prove what is required to be proved as a result.
3. Write the ‘Given’ section in a list form. This will make the given information more prominent in your eyes and it will be recorded in your brain more easily.
4. Write what has to be proved under the ‘To Prove’ section just below the ‘Given’ section.
5. Draw your constructions in the figure using dotted lines in order to differentiate them from the given figure.
6. Write your constructions under the ‘Constructions’ section below the ‘To Prove’ section in a list form. This will help the examiner to know about your constructions readily.
a. Do not write in a directive manner because you cannot ask your examiner to do something for you.
7. Finally, you are ready to write the ‘Proof’ section.
a. First of all, proof the whole thing in your rough work column (if you think you do not know the solution), because you may have to approach the problem in more than one way in order to arrive at the desired result. Do not have to write the steps completely. Think logically and complete the proof. Jot down the points serially.
b. Once you have figured out the correct approach, come to the fair area of your answer sheet and start writing.
c. Give a reason for every statement that you write in this section.
8. After completing the proof, end your answer by writing ‘hence proved’ or Q.E.D.
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