Stage 5 of GEOMGBITS: seven trials in the special triangles. Memorise just two constants — √2 ≈ 1.414 and √3 ≈ 1.732 — and every 45° and 30-60° triangle falls out of them, including the square’s diagonal and the equilateral’s height and area.
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 size a square’s diagonal, work a 45° brace in either direction, use the exact doubling in a 30-60-90, reach for 1.732 when the long leg is wanted, and get an equilateral triangle’s height and area from a single constant each.