Stage 4 of GEOMGBITS: seven trials in right triangles. Four remembered triples — 3-4-5, 5-12-13, 8-15-17, 7-24-25 — and their multiples replace a square root nearly every time. When none fits you estimate the root; when the shape is in doubt, you test it.
Each trial is locked until you clear the one before it. Every level scores out of 1000 — 600 for accuracy, 400 for speed — so speed alone can't clear the bar; you have to solve most problems, and quickly. Reach 650 to unlock the next.
You can spot a Pythagorean triple and its multiples on sight, run one backwards to find a missing leg, estimate a root when no triple fits, and test whether a triangle is right-angled at all.