GRE Geometry

Figures are not drawn to scale

A GRE diagram shows the configuration, not the measurements. An angle that looks like a right angle is not one unless it is marked or stated, and two sides that look equal are not equal unless told. Coordinate-geometry figures are the exception — those are drawn to scale unless stated otherwise.

• Redraw the figure to an extreme: make the angle very wide, then very narrow.
• If the relationship changes between your two drawings, the answer is "cannot be determined".
• Mark every given on your own sketch before reasoning.

The facts worth having cold

• Triangles. Angles sum to 180°. Any side is less than the sum and more than the difference of the other two.
• Right triangles. Pythagoras, plus the 3-4-5, 5-12-13, 30-60-90 and 45-45-90 ratios — the last two remove any need for trigonometry.
• Circles. Circumference 2πr, area πr². An inscribed angle is half the central angle on the same arc.
• Polygons. Interior angles sum to (n − 2) × 180°.
• Coordinates. Slope as rise over run; distance by Pythagoras on the differences.

A great many GRE geometry questions are solved by finding a right triangle inside the figure. Looking for one before reaching for anything else is a reliable first move.