Geometry Summary

GRE Quantitative · Axiom Academy

Key takeaways from Unit 4 — lines and angles through 3D solids and coordinate geometry, and how the GRE actually tests all of it. Geometry on the GRE rewards recognizing structure over memorizing formulas: parallel-line angle patterns, special right-triangle ratios, and inscribed-in-a-semicircle right angles let you skip calculation entirely. Every shape you studied connects to the ones around it — angles build triangles, triangles build polygons, triangles inscribed in circles create right angles , and 2D cross-sections build every 3D solid. Figures are NOT drawn to scale unless the problem says so — trust the given numbers and geometric properties, never how a figure looks on the page. Coordinate geometry is where algebra and geometry merge : circle equations, parabolas, and reflections describe the same shapes you drew by hand, now as equations on the plane. These aren't just test-day tricks — the same relationships (triangulation, load-bearing angles, tolerances on curved surfaces) are exactly what engineers and designers use to build real structures. Complementary angles sum to 90° , supplementary angles sum to 180° , and vertical angles are always equal. When a transversal crosses two parallel lines, every acute angle formed is equal to every other acute angle (and likewise for obtuse) — one given angle unlocks all eight. When to use: any figure showing parallel lines or intersecting lines

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