What can you assume on GRE geometry diagrams, and what can’t you assume?

What you can assume:

Assumption 1

Lines appearing straight can be assumed to be straight


Even though from the adjacent figure you may feel a definite urge to say that AB is straight, maybe in reality there is a tiny bend which makes the angle ADB = \(179.99^o\)or A-D-B non collinear. Therefore, it is hard to say with certainty that angle x is \(180-120 = 60^o\) . Fortunately in GRE, you are allowed to assume that lines which appear straight can be assumed to be straight. Based on the above assumption, it can be deduced from the adjacent figure that the angle x is definitely \(60^o\).

Word of Caution:
BTW, don’t confuse “straight” (meaning, “lying in a line, collinear”) with “horizontal.” Many people say “straight” when they mean “horizontal”, and this is a 100% wrong mistake that leads to a great deal of confusion. For example, you must assume a line on the GRE is “straight”, but you absolutely cannot assume it is “horizontal” if that is not stated.

Assumption 2

A polygon in GRE has a) closed shape and the sides don’t “cross” each other and that the figure is “convex” (all vertices pointing outward), not “concave” (some vertices pointing inward).

Assumption 3

Unless otherwise stated any angle in the GRE diagram refers to the smaller angle.

Therefore in the adjacent figure, if nothing is mentioned about angle BAC, it's value is equal to \(x^o\) and not \(y^o\).

What you cannot assume

Visual estimation on angles

Do not assume values angles unless otherwise stated


For example, you may seem to have a strong urge to assume that the angle x in the left-hand side figure to be \(90^o\). However, it is one the most famous traps of GRE to dupe students into making this mistake. Unless otherwise explicitly stated, for example in the right hand side figure where you can take angle x to be \(90^o\).











Do not assume numerical comparison of angles based on visual estimation

For example, in the left-hand side picture the only things you can assume are as follows:

1. \(y + x = 180^o\)
2. \(y,x> 0\)
3. y is greater than x

You can assume that the line AB which appears straight is straight meaning \(y+x = 180^o\) and both the angles are positive. However, assuming that y is greater than x based on the diagram will be a fatal mistake which will rob you off your dream 170 score in quants.

Parallelism

If not stated explicitly, you cannot assume parallelism.

Based on the adjacent figure, it will be wrong to assume that line \(l_{1}\) is parallel to \(l_{2}\).

Deduction vs Assumption

Finally, it’s important to know the theorems and the defined properties of shapes. For example, if you are told that two angles in a triangle are equal, then by that extraordinary theorem, the Isosceles Triangle theorem, you also know the two opposite sides are congruent. If you are told that a figure is, say, a rhombus, then you automatically know it has all the defined properties of a rhombus (four congruent sides, congruent opposite angles, perpendicular diagonals). Technically, if you know something as the result of a definition or a theorem, then you are deducing it, not assuming it, but this is still in the broad categories of things you need to know about your diagram that were not explicitly stated.

Summary

Just to wrap up this interesting topic, the following points or take way should be always in your head while tackling GRE geometry questions:

• Figures not necessarily drawn to scale
• Avoid visual estimation

Be very clear on what you can assume and what you can’t assume — I would guess that over 80% of all the mistakes that folks make on GRE Geometry problems involving diagrams result from improper assumptions.

Try the practice questions below to get a hang of the fundamentals discussed above!! Good luck !