Geometry

Section: Geometry Estimated study time: 45 minutes Content: GRE Geometry covers lines, angles, triangles, quadrilaterals, circles, and coordinate geometry. The GRE does not test trigonometry or 3D geometry beyond basic volume/surface area formulas. All diagrams on the GRE should be treated as approximately accurate for the general shape, but NOT necessarily drawn to scale — never assume lengths or angles from visual appearance unless the problem states specific values. Lines and angles: vertical angles are equal. Supplementary angles sum to 180°; complementary angles sum to 90°. A transversal crossing two parallel lines creates equal alternate interior angles and equal corresponding angles. The sum of all angles in any triangle is 180°. Triangle properties are heavily tested. The Pythagorean Theorem (a² + b² = c², where c is the hypotenuse) applies only to right triangles. Memorize Pythagorean triples: 3-4-5, 5-12-13, 8-15-17, and multiples thereof. Special right triangles: 45-45-90 (sides in ratio 1:1:√2) and 30-60-90 (sides in ratio 1:√3:2). The triangle inequality: the sum of any two sides must be greater than the third side. The area of a triangle = ½ × base × height. For an equilateral triangle with side s: area = (√3/4)s². Similar triangles have equal corresponding angles and proportional corresponding sides. If triangles ABC and DEF are similar with ratio k:1, then corresponding sides are in ratio k:1 and areas are in ratio k²:1. The altitude from the right angle in a right triangle to the hypotenuse creates two smaller triangles, each similar to the original and to each other. Circles: area = πr², circumference = 2πr = πd. Arc length = (central angle / 360°) × 2πr. Sector area = (central angle / 360°) ×…