Strategy: "Not Drawn to Scale" and Figure Discipline

The Single Most Important GRE Geometry Convention

Per the official GRE Math Conventions, geometric figures such as triangles, circles, and angles are not necessarily drawn to scale. The figure shows how objects are connected — which points are on which line, which angle is inside which triangle — but you must never measure the drawing to estimate a length or an angle. There is one exception: coordinate systems, number lines, and data figures (bar graphs, etc.) ARE drawn to scale.

Strategy 1: Trust the Text, Not the Picture

Read every given number from the wording, and treat the figure only as a wiring diagram. If a triangle looks isosceles but no marks or numbers say so, it isn't necessarily isosceles. A figure that looks like a right angle is only a right angle if a small square is drawn or the text states $90°$.

Strategy 2: Redraw to Break False Assumptions

Because figures can be misleading, a powerful QC tactic is to redraw the figure at an extreme while keeping every stated constraint. If a triangle's angles are only partly fixed, sketch it once "tall" and once "flat." If the compared quantities swap order between the two legal drawings, the answer is (D).

Strategy 3: Look for the Hidden Right Triangle

Rectangles, squares, and the diameter of a circle constantly hide right triangles. A rectangle's diagonal splits it into two right triangles, so a $12 \times 5$ rectangle has diagonal $\sqrt{12^2 + 5^2} = 13$. Recognizing Pythagorean triples (3-4-5, 5-12-13, 8-15-17) saves computation.

Strategy 4: Convert Circle Facts in One Step

Circle questions give one measurement (area, radius, diameter, or circumference) and ask for another. Always route through the radius: $A = \pi r^2 \;\Rightarrow\; r = \sqrt{A/\pi}, \qquad C = 2\pi r.$ Keep answers in terms of $\pi$ until the very end; the GRE usually lists choices as multiples of $\pi$.

Strategy 5: For Solids, Track Units and Dimensions

Volume scales with the cube of a length, surface area with the square. If a cube's edge doubles, its volume grows by $2^3 = 8$ and its surface area by $2^2 = 4$. GRE QC frequently tests exactly this scaling intuition, so reach for the exponent rather than recomputing from scratch.

Strategy 6: Estimate With $\pi \approx 3.14$ Only at the End

When a numeric (non-$\pi$) answer is required, keep symbolic $\pi$ through the algebra and substitute $3.14$ (or use the on-screen calculator) only in the final step to avoid rounding drift.