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How To (Not) Ace Geometry

by Benjamin Sheng

Geometry, what Kepler called “the archetype of a perfect world”. If only the class itself could be a part of that perfect world – when I took the class, I once got 4/10 on a proof because I missed 6 steps out of 16. Memorizing the theorems is difficult and the proofs are grueling. How do you pass? Or even better, how do you ace the class? To spare you the feelings of consternation that you may experience, I will provide some advice to help you on your geo journey.

1.  In geometry, you will often have to prove statements. Let’s face it, proofs are terrible and no one wants to do them. What’s more, if they’re giving you a statement to prove, it must be true. There’s no need to prove it yourself.

2.  The same goes for constructions. Just draw random lines and arcs. Trust me, no one will know the difference. As long as it looks fine, it will serve its purpose. See Advice No. 5.

Even Euclid couldn't have done it better!

3.  Know the five essential postulates of geometry:

  • Two points can be connected, or disconnected, in any way you want.
  • A line can be extended into any shape, or even a point.
  • You can draw a circle if and only if a square and a triangle, as well as a nonagon, have a common center.
  • ALL angles are congruent.
  • All lines are parallel, but some lines are more parallel than others.

4.  In the event that you do have to prove a statement step by step, but forget the name of an essential theorem, make up your own: it’s not that hard. Hence, the Point Trisector Theorem and the Law of Binary Circles.

5.  Know your triangle congruences and similarities. However, to be honest, just arrange the letters ‘A’ and ‘S’ in three-letter strings for congruences and two letter strings for similarities. 

6.  In geometry, you’ll be working with circles and solids with circles a lot. It greatly simplifies your calculations to round π to 3. How come no one thought of it before? (Disregard the fact that Indiana nearly did so in 1897). Doing this also greatly improves the formula for the volume of a cone – it becomes r²h. Who wants to deal with ugly decimals?

7.  All figures are drawn to scale. That bears repeating. ALL FIGURES ARE DRAWN TO SCALE. In the unlikely scenario that a diagram says “Figure is not drawn to scale”, ignore it – they’re just trying to throw you off. When solving problems involving these figures, measure side lengths with a ruler. If you unfortunately don’t have a ruler, measure distances between your fingers. 

What’s more, if two lines look parallel, they probably are. If two triangles look congruent or similar, they probably are. You get the idea, right?

8.  Trigonometry might be the worst part of geometry. When evaluating trigonometric functions, it doesn’t hurt to round everything to the nearest one. Then, the value of all trigonometric functions become 1, 0, or -1, which drastically cuts down the clutter. If Archimedes can calculate the circumference of the Earth using a Syracusian well, then a few rounding errors certainly won’t make a difference.

9.  Your teacher might ask you to bring quintessential geometry supplies to class such as rulers, compasses, protractors, and your textbook. Using these supplies for math is boring. Why not use them for sword fights? It’s always entertaining to charge at each other with lances leveled and shields raised in the middle of class (please don’t stab anyone with a compass).

Duel of the Geometricians

10.  Some geometry classes have a small probability unit, which will probably be the easiest one. The answer for every probability question is ½ because there are always only two choices – either something happens or it doesn’t.

You don’t want to spend a year in a boring class. It’s up to you to make class fun 😉

*Disclaimer: None of the above advice is intended to be taken seriously. The author is not responsible for any incidents that may occur from implementing said advice.


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