The first rule of life? Life (as well as geometry) can be difficult. But why make it more difficult than it has to be? Here are 11 tried-and-true tips to make your forays into the world of geometry as painless as possible.
1. Use a Clear Plastic Protractor
Tools are fun, and the dandy protractor is no exception. The clear plastic kind is especially handy because you can see through it. That way, you can extend your angles right through the scale of the protractor. Reading angle measures is much easier then.
2. Use a Clear Plastic Ruler with Inches and Centimeters
Just as with a clear plastic protractor, with a clear plastic ruler, you can extend your lines, which makes getting their measures easier. Using a ruler with inches and centimeters is a good idea. Go metric, baby!
3. Buy Thyself a Compass
You need to have a protractor for your angles and a ruler for your straight lines. You also need a compass — for those curved lines. Look for one that has a ruler right on it. That way, you don't have to use both the compass and a separate flat ruler when making a circle. Just pull the compass apart the distance you want and use the built-in ruler.
4. Get a Good Pencil to Draw Fine Lines
You need a pencil to make accurate drawings. Try to find a technical drawing pencil with a .05 mm lead. An eraser is an important commodity, also. You won't regret getting one that has a brush. Eraser residue leaves the page easier when it's brushed away.
5. Buy Thyself a Good Scientific Calculator
Never underestimate the power of a good scientific calculator — the kind with sin, cos, and tan keys. You're going to need those keys on trig days. Square root and squared keys are useful for all that triangle stuff. And fresh batteries are a good idea on test day.
6. Write Down Your Givens and Wants
When you're setting up to solve a problem, be it a proof or just an equation, write down everything you're given to work with even if it doesn't seem important. The smallest details can lead to the biggest revelations. After you finish with what you've been given, move on to what you want. Write that down, too.
7. Make Diagrams
A picture is worth a thousand words. Make a diagram with your awesome technical pencil. Try to draw things in proportion, keeping your spatial relationships intact. Mark off everything in the drawing that is in your given. If you have congruent lines, congruent angles, or parallel lines, mark 'em.
8. Develop a Plan of Attack
You have your given. You've written down what you want. You've drawn your diagram. Now you have to develop a plan to solve the proof. A plan of attack can be everything from which auxiliary lines you need to draw to the type of reasoning you're going to use to solve the proof. If you develop a plan before you start, it gives you direction and saves on the number of steps you'll have to take to get from the given to the prove statements.
9. Read Through the Statements
This suggestion works best with completed proofs — proofs actually completed by someone else, like in a book. Read through the numbered information in the Statements column. Try to figure out what the reason should be for each statement. Check to see whether you're correct. If you are, go on to the next statement. If you aren't, figure out why the reason is what it is before you proceed. Going through the steps without having to create them and just trying to understand the logic behind them is the best way to get a handle on complex proofs.
10. Apply Geometry Objects to the Real World
Apply the objects of geometry to the real world as you learn about them. Make everything a mind game. For circles, think pizza. For rectangles, think tennis courts. For spheres, think baseballs. You get the idea. Associating the information to something you already understand not only helps speed up your understanding but also improves your chances of keeping the info in your memory. There are lots of things to remember in geometry. It's time to expand your mental capacity.
 | 11. Play Pool! |
This final tip is here to give you a good example of how to apply geometry to the real world. Pool is all about angles. Hit the ball off one bumper at a certain angle, and it may hit another ball. Change the angle and you may hit the ball so that it rebounds from one bumper to another and sinks a solid colored ball. You may scratch or mistakenly sink the 8 ball. So play pool — angles, angles, angles!
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