🎓 Ages 15–18 · Grades 9–12 · Geometry

LocusForge

Geometry is where "it looks true" becomes "here’s why it’s always true." Here you conjecture the measure a theorem guarantees — an angle, a length, an area — commit to it, and a deterministic engine confirms the invariant and names the theorem that proves it. No jargon, nothing sent anywhere, and a wrong conjecture is just where the proof starts.

The Geometry Lab ★ the main event

Read a figure across angles, triangles, circles, similarity, right-triangle trig, and polygons — conjecture the measure, then a pure engine confirms it and states the theorem that proves it. Because it’s computed, not eyeballed, the invariant is exact.

Open the Geometry Lab →

Who you’ll meet

Not mascots — everyday geometers, each showing one idea in action. You’ll run into them across the lab and the kits.

  • Pell — builds figures with only compass and straightedge (constructions)
  • Vireo — proves triangles congruent from the givens (SSS/SAS/ASA)
  • Orin — reads right-triangle ratios and the unit circle (trig)
  • Osgood — relates inscribed and central angles (circle theorems)
  • Talise — proves it on the coordinate plane (distance, midpoint, slope)
  • Castell — moves figures by rigid motions and dilation (transformations)
  • Alba — slices solids and cones into cross-sections
  • Renard — turns "it looks true" into "here’s WHY" (proof)
  • Adisa — the mentor — conjecture from the drag, then prove it

Check what you know

Sixteen short kits — constructions, angles & lines, triangle congruence, similarity, right-triangle trig, the unit circle, circle theorems, coordinate geometry, transformations, quadrilaterals, area, solids, conics, vectors, and proof — anchored to HS geometry. Hints when you want them; progress stays on this device.

1. Constructions Constructions — compass and straightedge · 25 questions 2. Angles & Lines Angles and lines — parallel lines and angle relationships · 25 questions 3. Triangle Congruence Triangle congruence — SSS, SAS, ASA, and CPCTC · 25 questions 4. Similarity Similarity — same shape, proportional size · 25 questions 5. Right-Triangle Trig Right-triangle trigonometry and the Pythagorean theorem · 25 questions 6. The Unit Circle The unit circle — angles and coordinates · 25 questions 7. Circles & Circle Theorems Circles — inscribed and central angles, chords · 25 questions 8. Coordinate Geometry Coordinate geometry — distance, midpoint, and slope proofs · 25 questions 9. Transformations & Symmetry Transformations — rigid motions and dilation · 25 questions 10. Quadrilaterals Quadrilaterals — properties and classification · 25 questions 11. Polygons & Area Polygons and area — perimeter, area, and regular polygons · 25 questions 12. 3D Solids & Cross-Sections Three-dimensional solids — volume, surface area, and cross-sections · 25 questions 13. Conic Sections Conic sections — slicing a cone · 25 questions 14. Vectors Vectors — magnitude, direction, and operations · 25 questions 15. Proof & Justification Proof and justification — from conjecture to certainty · 25 questions 16. Capstone: The Locus Problem Capstone — conjecture and prove a locus or construction · 25 questions

How it works

LocusForge trusts you — it’s about reasoning from givens to a proof, not memorizing, and a wrong conjecture is just a place to learn. Every measure is computed by a small deterministic engine (no server, nothing sent anywhere). Your progress is saved only on this device: no accounts, no ads.