Using Figures to Solve ACT Geometry
Wondering what you’ll face on the Math section of the ACT? While the test makers openly admit that algebra is the most commonly tested subject here, there’s another not too far behind: geometry. (The ACT averages 33 algebra, 23 geometry and four trigonometry problems.)
Because many geometry questions require at least a bit of algebra to solve them, we can use a three-step process similar to the one used for algebra:
- Step 1: Know the Question
- Step 2: Let the Answers Help
- Step 3: Break the Problem into Bite-Sized Pieces
To tailor these steps to geometry problems, we recommend one small change: using figures.
Use the Figures — Or Draw Your Own
When faced with a geometry problem, transfer all of the numbers provided in the question into their corresponding places on the figure. Did the question give you a blank triangle, but told you the values of two of the angles in the accompanying description? Write those numbers on the figure! Encounter a problem that doesn’t have a figure? No problem — draw your own! When asked to determine angles or measurements, having a figure to guide you will be an invaluable resource. Plus, it gives you a place to more accurately assess what information you have versus what information you need to solve the problem.
Once you’ve done this, write down any formulas you need and fill in any information you have. For this particular example, if the ACT asks you to find the area of that triangle, you might know in your head that you need the length of the base as well as the height of the triangle, but unless you write the measurements down as you find them, it’ll be all too easy to get those numbers jumbled in your noggin. (Note that the ACT won’t typically provide you with the formulas you need. The test will provide weird formulas — such as the surface area of a sphere — but you’ll be expected to know how to find simpler features such as the circumference of a circle.)
To Scale or Not to Scale? (That Is the Question)
If no numbers are given for a figure, you may still be able to extract information from it. You will, however, have to first determine whether it’s drawn to scale. The test creators make a big deal in the instructions about the fact that their figures are not necessarily drawn to scale. Here’s the thing, though: they usually are — or they’re at least close enough that you can use them in broad strokes.
Even if you can’t determine the exact scale of a figure, you may still be able to use Ballparking to narrow your choices. Choosing the correct answer doesn’t always rely on you calculating a precise value — often it will be clear that some of the answers are either too big or too small, and therefore you can eliminate those just by using the figure instead. This can help you move through the Math section at the pace you need.
Brushing up on what content the ACT will throw your way is half the battle of efficient test prep. And if you want to determine which areas you know well and which areas might benefit from a little more practice, a free practice test can help! For more strategies on how to navigate the Math section of the ACT, as well as tips and tricks for every section of the test, check out our book Cracking the ACT.