Estimations and assumptions. So on the ACT, what are we allowed to assume from diagrams, and what are we not allowed to assume? Well, this is tricky. The ACT does not officially confirm this, but it appears that all the geometry diagrams on the test are drawn to scale. Show Transcript
Now, that's really huge. That's a tremendously important fact to appreciate. Because the diagrams are almost always drawn to scale, you can use estimation in geometry problems. You can estimate lengths and angles. As with numerical estimation, it's rare that you will be able to solve a question entirely, purely with visual estimation.
Nevertheless, visual estimation can be a good way to eliminate a few answers, and it can be a good confirmation of any calculations you do. If you take the paper-based ACT, you can use that to help yourself in a few ways. For example, we can use the corner of the answer sheet as a right angle, to compare to see how close an angle on a problem is to a right angle. We could also mark a known length lightly On the edge of a sheet then use that to measure whether another length is bigger or smaller.
So, for example suppose we have this problem. And suppose we were running out of time or we didn't know how to solve it. We actually will solve this problem later on in the diam tree module. But pretend we didn't know how to solve it. Well, certainly, we could measure this length. This length is six.
And so this length here we can see it's bigger than six. So we can eliminate two answers. We can also measure this length here 14 and we'd see that GF is a little smaller than 14. So GF certainly can't be larger than 14, it certainly can't be 18. So right away just with very basic estimation, we could eliminate three answer choices.
And we'd be in very good shape to guess, even if we didn't know how to solve the problem. Here's another practice problem. So in this one a is 6 and b is 8, what does c equal? Well, by doing some basic measurements, in fact, we don't even have to do very sophisticated measurements.
We can see that whatever c is, it's smaller than 6 and so it's certainly smaller than 8. And so any of these numbers like 10 and 14 these are right out. Now we have three other answer choices here. It's hard to say exactly how big these radicals are, but at least for estimation purposes we can clearly eliminate two answer choices.
Also notice that if you did some kind of calculation, you said, oh, it's a 6, 8, 10 triangle. Well, you could immediately eliminate 10. You could realize that that wasn't the correct answer. Because c here is not the hypotenuse, in fact it's the smallest side. And the smallest side cannot be ten.
Most or all of the geometric diagrams on the ACT are drawn to scale. So you can use visual estimation to eliminate answers, and to confirm any calculations you do. Always be thinking about possible ranges of sizes of line segments and angles, when you look at a diagram on the ACT.