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Hard Geometry & Possibility

Geometry problems at the end of an SAT and ACT Math section can be hard for two reasons.

First, you may not have done plane geometry (perimeter, area, angles, etc.) for a number of years – perhaps since middle school – so a hard geometry problem will be that much harder due to your unfamiliarity.
Second, even if you are familiar with the concepts and formulas you’d need to solve these geometry problems, you may still struggle with these questions because the way forward is unclear. If you knew what to do, you could do it, but that’s the challenge – knowing how to break down the problem and generate the procedure to solve it is the real battle.

In this exercise, I want to show you a way to narrow down the possible paths to the solution in a systematic way. First, try this problem:

And then watch this video for the solution and the strategy discussion:

About the Author:

I’m Rob Schombs, the founder of Reason Prep, creator of these videos, and your test prep tutor. I earned a BA in Chemistry (2006) and an MA in Science and Technology Studies (2009) from Cornell University. In 2010 I started tutoring SAT, ACT, math, chemistry, and writing full-time, and Reason Prep followed shortly after!