Draw A at top in the isosceles-right and 30-60-90 figures#95
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The "or miss entirely" alternative conflated Ssu's actual failure mode (non-uniqueness via two solutions) with simple data inconsistency. The two-solutions case alone is what shows the b > a hypothesis is essential. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Forward direction now also mentions the projection-of-A choice of M (Ssu, right angle opposite the hypotenuse) and the angle-bisector choice (sus), in addition to the existing midpoint+sss proof. Inverse direction adds the angle-bisector variant (usu again) and a brief note that midpoint doesn't help here because the angle would land opposite the potentially shorter AM. Applied across cs, en, sk. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
The handout intro promises triangles will be drawn with vertex A at the top. The isosceles right triangle is reoriented so A is the top apex with the right angle pointing down. The 30-60-90 figure gets an A↔C label swap (geometry unchanged) so A sits at the equilateral apex; the proof in cs/sk/en is mechanically re-labeled to match, including the Thales remark on the hypotenuse AB. Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
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Summary
The handout intro of
angle-basics-1states triangles will be drawn with vertex A at the top — the international/olympiad convention. Two figures violated this:angles-isosceles-right-triangle: now reoriented so A is the top apex with the right angle pointing down, and B/C are the base corners (legs |AB|=|AC| preserved, 45° marks at B and C). Prose untouched — it only refers to vertices abstractly.angles-90-60-30: A↔C label swap with identical geometry. A is now the equilateral apex on top; C is the bottom-middle right-angle vertex; B and B' flank C on the base. The cs/sk/en proof body gets the same mechanical A↔C swap — including the Thales remark, which now correctly namesABas the hypotenuse.The cs/sk/en handout JSONs are regenerated to match.
Sibling 3rd figure that the same audit identified —
angles-sas-proof— is left as-is on purpose: putting A at the apex there would have meant rewriting the SAS-construction proof to start from B instead of A, which felt less natural than the current "construct from vertex A" framing.🤖 Generated with Claude Code