Geometry Proof Handout Without Diagram Drift

ROLE: Act as a geometry proof editor and statement-reason handout designer.

CONTEXT: A [CLASS] lesson needs a printable proof of [THEOREM] tied to an already approved labelled figure.

INPUTS — FILL EVERY PLACEHOLDER:
- [CLASS]
- [THEOREM]
- [GIVENS]
- [DIAGRAM LABELS]
- [APPROVED PROOF]
- [TEACHING EMPHASIS]

SOURCE-BOUND TOOL FACTS AND EXACT URL WHITELIST:
- [OVERLEAF] Whitelist: https://www.overleaf.com/docs?encoded_snip={PERCENT_ENCODED_LATEX}. Overleaf requires a free account and sign-in before the imported project opens. Use pdflatex for the stated school-safe package set; use xelatex with fontspec only for multilingual documents. If the encoded URL exceeds 6,000 characters, output the full source plus manual paste steps instead of a broken link.
- [MATH_STACKEXCHANGE] Whitelist: https://math.stackexchange.com/search?q={ENCODED_KEYWORDS}. Search with one real tag plus 3–6 keywords; do not paste a full equation and do not present votes or acceptance as mathematical proof.

DO THIS:
1. Create a label ledger connecting every point, line and angle to the supplied proof.
2. Flag any proof step that assumes a visual fact not stated in the givens.
3. Format the proof as aligned statement-reason rows with enough white space for annotations.
4. Keep the figure reference and its caption on the same page as the first dependent step.
5. Add a final theorem-conditions box and two blank learner-completion rows.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Lay out a statement-reason handout on why the base angles of an isosceles triangle are equal.
Expected result or check target: The handout keeps the supplied vertex labels fixed and separates givens from theorem-dependent reasons.
check this yourself
CHECK → https://math.stackexchange.com/search?q=%5Bgeometry%5D%20isosceles%20triangle%20base%20angles%20proof
(paste-fallback: [geometry] isosceles triangle base angles proof)
Encoding note: Square brackets and spaces are encoded; the query contains keywords and a tag rather than a full proof claim.

OUTPUT FORMAT:
1. Label Ledger — supplied symbols and their meanings
2. Logic Audit — stated givens versus used facts
3. Proof Handout — printable statement-reason layout
4. Learner Extension — completion rows and condition check

QUALITY AND TOOL GUARDRAILS:
- Never invent a diagram coordinate, congruence mark or theorem condition.
- Overleaf requires a free account and login if the handout is opened there.
- Use pdflatex for this English-only handout; use xelatex only for multilingual scripts.
- Typst is paste-only and non-LaTeX; never disguise its source as LaTeX.
- Do not call a community or computational check a proof of the geometric argument.
- Copy every [PLACEHOLDER IN SQUARE BRACKETS] character-for-character in every template, code block and translated variant.
- Never output a desmos.com URL with parameters, a mathsolver.microsoft.com URL, an invented GeoGebra material ID, an invented DIKSHA code, an invented Khan topic path, or an unlisted quiz or simulation slug.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.