So the first and the second part of this article is already done and dusted. If you haven’t checked them out already, we would suggest you do that first, and then move on to this one right here. This is the 3rd and the final part of this article. So let’s begin without further ado.
10. Develop a solution plan
In part 2 of this article, we mentioned that you should write down the things that are “given” in the problem and the things that need to be “found/proven” separately on a piece of paper (your answer sheet, to be more specific).
As soon as you note down those “givens” and the “wants”, you need to develop an organized plan of approach for your solution within a few seconds of time.
At first determine whether it is a proof or a problem that wants you to find the unknown. [Remember that your entire approach should be based on the type of your problem (proof or “find the unknown”)].
Then, think about the concepts and the formulae that can help you out in your situation. Write them down systematically on your answer sheet for an easy reference. Practice these habits religiously, and you will get the results in no time.
11. Learn about supplementary and complementary angles
Supplementary angles are those angles that add up to make 180 degrees in particular.
Complementary angles, on the other hand, consist of the ones that add up to make 90 degrees on the whole.
A few more things to remember:
Vertical angles are always congruent to one another.
In the same way, interior and exterior alternate angles are also congruent to one another.
12. Memorize the basic trigonometric formulae for the sines, cosines and the tans of a right angled triangle
Make sure you remember the three basic trigonometric formulae as closely as possible. These will come in handy for your geometrical solutions.
Consider a right-angled triangle ABC like this one right here,
On the basis of the figure depicted above,
Sin θ= opposite / hypotenuse= AC / AB.
Cos θ= adjacent / hypotenuse= BC / AB.
Tan θ= opposite / adjacent= AC / BC.
13. Apply the concepts of geometry in the real world
There are lots and lots of things to remember in geometry, ranging from formulae to concepts, to postulates and so on.
The best way to improve your geometrical vocabulary, on the whole, is to find a connection between the subject and the real world.
Geometry is everywhere. You would just need to keep an eye out to find out the same.
For example,
As soon as the topic of circles comes up in a problem, think of the same in the form of a pizza. For rectangles, think in terms of a tennis court. For spheres, think footballs, and so on. Remember, imagination is your only limitation.
Note: By connecting real life objects with the textual world, you are simplifying the matter for your own good. So turn this practice into a habit. It can benefit you a lot in the long run.
14. Know the Pythagoras’ theorem in precise detail
The Pythagorean theorem is wholly based on the properties of a right angled triangle.
Here’s what it says-
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
[Hypotenuse= The immediate side opposite to that of the right angle.]
The theorem is explained below with a diagram for better comprehensibility:
Consider the right-angled triangle given in the figure below,
According to the Pythagorean theorem,
(Hypotenuse)2 = (Perpendicular)2 + (Base)2
= (AB)2 = (AC)2 + (BC)2
Just make sure you remember this theorem in precise detail. It can help you a lot to find out the missing angles in several geometrical problems.
15. Last but not the least, seek extra help if you want
Sometimes, you may need that extra help in life to succeed in your academics. Class lessons might not be enough in such circumstances; you may require something more. Private tuitions can be an excellent idea if you really want to pursue one.
Working with someone one-on-one can be very useful in comprehending difficult materials, and a tutor is no different either. So don’t hesitate to seek extra help if you really feel you need one.
So that’s it for the final time now. It’s time to bring this entire article to a close for now. Hope you had a good and useful read.