# Common GMAT mistakes - Geometry

## Z53.png By Brent Hanneson - May 15, 2020

Making incorrect assumptions about geometric diagrams

When it comes to Geometry questions, there isn't a lot you can assume.  For example, lines that appear to be parallel, angles that look 90 degrees, and sides that look equal aren’t necessarily so.  This, however, doesn’t mean we can't make any assumptions about geometric diagrams on the GMAT. For example, if a line appears to be straight, we can assume it’s straight. Likewise, if a point appears to be on a line, we can assume that it is so. For more on what can and can’t be assumed on the GMAT, watch this video.

Not taking advantage of diagrams drawn to scale

As you probably already know, the GMAT has two types of math problems: Data Sufficiency questions and Problem Solving questions.  If a geometric diagram appears in a Problem Solving question, then we can assume it’s drawn to scale, unless we’re told otherwise (e.g., figure NOT drawn to scale). This is a huge gift, yet I don't see many students taking advantage of this helpful feature. In some cases, if the answer choices are reasonably spread apart, estimating a length or angle may very well be the fastest way to reach the correct answer. More importantly, if you have no idea how to solve a geometry question, estimating a length or angle may allow you to quickly eliminate 2 or 3 answer choices and significantly increase the likelihood of guessing correctly. For example, here's my solution to an official GMAT question in which we can use a very vague approximation to eliminate 4 of the 5 answers choices.

Not memorizing 3 useful approximations

As part of the above estimation strategy, all students should have the following approximations memorized for test day:

• The square root of 2 is approximately 1.4
• The square root of 3 is approximately 1.7
• The square root of 5 is approximately 2.2

These approximations can save you some time, so memorize them immediately.

Not knowing the formula for area of equilateral triangle

I'm not a big fan of memorizing tons of formulas, but this particular formula can save you a lot of time on test day:

Area of equilateral triangle = (sqrt3)(side²)/4

Students who don't know this formula are forced to make some additional calculations in order to apply the standard base-times-height-divided-by-two area formula we're all familiar with.

Not mentally moving points and lines on data sufficiency questions

When it comes to Data Sufficiency questions involving geometric shapes, determining sufficiency often involves confirming whether the statements "lock" a particular angle, length, or shape into having just one possible measurement. So, in some cases, we can avoid performing lengthy calculations and, instead, mentally move unfixed parts of the diagram to see whether doing so changes the answer to the target question. This concept is discussed in much greater detail in this video.

Not knowing that a square is also a rectangle, parallelogram, and rhombus

This one isn't really a big deal; it's more of a pet peeve :-)

Cheers, Brent