The makers of the SAT, believe it or not, are not out to get you. They do play tricks and try to lure you in with some wrong answers, and that feels devious at times, but you have just about everything you need to answer the questions in front of you on the SAT. They even go so far as to give you a set of formulas at the beginning of every math section. What they give you is a set of geometric facts dealing with area formulas and right triangle proportions. The latter comes up quite a bit on the test.
The funny thing is, most test takers don’t even bother to look at that information for more than a moment, and many forget they are there even though they can come in handy.
What Formulas You’re Given
The first three are very basic: the area of a circle, of a rectangle, and of a triangle. On your actual SAT test date, you shouldn’t need to reference these—get them down pat before you take the test and you’ll be much more efficient.
The next two, the areas of a cylinder and a box, are slightly less well known but not any less basic. Just multiply the 2-D area of one side by the extra dimension.
Then comes the Pythagorean theorem. Again, this should be cemented in your brain. . Cake.
The last two are not memorized often enough, though, and they come up constantly on the SAT. There are two special right triangles, 30°-60°-90° and 45°-45°-90°, and you are going to need their proportions, possibly a few times. Remember to go back and look at the reference information at the beginning of the section any time you see a 30, 60, or 45 in a triangle. If you’re already really confident with the info, great—just remember to keep an eye out for those angle measurements.
They also tell you that a circle totals 360°, clearly, and a triangle’s angles total 180°. That second fact is also crucial to remember. The SAT loves triangles.
Formulas You’ll Need to Memorize
Parallel lines crossed by a transversal have a lot of equal angles:
In this image, m and n are parallel. If you see that information on your SAT, you’re going to be able to fill in a whole lot of other information really quickly.
A line from a tangent’s point of intersection to the circle’s center makes a right angle with the tangent:
This will come in handy when dealing with some complicated figures that require you to fill in a lot of measurements based on a bit of starting info.
And a regular hexagon can be broken into six equilateral triangles:
This doesn’t come up very often. You may see it once on your SAT, but it’s worth knowing ahead of time so you don’t have to come to the conclusion yourself. Note that it’s not just the angles that are equal, above; every shorter line segment is also equal.
Some combination or another of the formulas and facts mentioned here will give you the answer to almost every geometry question on the SAT. Be comfortable with them, and be ready to reference those special right triangle proportons.
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About Lucas Fink
Lucas is the teacher behind Magoosh TOEFL. He’s been teaching TOEFL preparation and more general English since 2009, and the SAT since 2008. Between his time at Bard College and teaching abroad, he has studied Japanese, Czech, and Korean. None of them come in handy, nowadays.
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