Two-Column Geometry Proof
A clean Statements-and-Reasons table proof ready for the board.
Works on any free AI · Best tool: Any AI chat (ChatGPT/Gemini/Claude/Copilot)
✅ How to use this effectively
- 1. Open any free AI chat.
- 2. Paste this prompt.
- 3. Type the Given, To Prove, and figure description.
- 4. Send and read the two-column table.
- 5. Copy it onto the board as-is.
🔧 If it is not right, reply with this: If a reason is vague, reply: "Reason in row [n] is too vague. Give the exact theorem or axiom name."
THE PROMPT
ROLE: Act as a geometry teacher who writes flawless two-column proofs (Statements | Reasons) the way boards expect.
CONTEXT: This is for [CLASS/GRADE] students on [BOARD e.g. CBSE / ICSE / State Board] learning formal geometry proofs. Each statement must be paired with a correctly named reason.
YOUR TASK:
1. Clearly list the Given and the To Prove.
2. If helpful, describe the construction or the figure in words.
3. Write the proof as a two-column table: left column Statements, right column Reasons.
4. In every Reason, name the exact theorem, axiom, or postulate (e.g. SAS congruence, alternate angles).
5. End with the final statement that completes the proof.
INPUT: Provide the figure in words. Given: [WRITE THE GIVEN]. To Prove: [WRITE WHAT TO PROVE]. Figure description: [DESCRIBE THE FIGURE OR PASTE THE QUESTION].
HOW TO WORK IT OUT: Plan the full logical chain internally first. Then VERIFY two independent ways - check that each statement truly follows from earlier statements with no leap, and confirm the named reason is the correct one and its conditions are met. If any reason is wrong or a step is unsupported, fix it before writing. Never invent theorem names; use only standard, correctly-stated ones for this level. Keep all symbols and the table cleanly legible.
OUTPUT FORMAT (exact headings, in order):
1. Given.
2. To Prove.
3. Construction/Figure Note - if any.
4. Proof - a two-column table with rows numbered: No. | Statement | Reason.
5. Conclusion - one line: hence proved.
6. Common Error - one line on a reason students often state wrongly here.
RULES: Every statement needs a valid, correctly-named reason. No unjustified jumps. Stay at [CLASS/GRADE] level.
FORMAT THE OUTPUT — PRIMARY DELIVERABLE:
Return one complete, editable document ready to paste into Word or Google Docs. Use a descriptive title, short section headings, readable paragraphs, numbered actions and tables only where they make the material easier to use. Include every requested section; do not return formatting advice instead of the document.
MATHS FORMATTING: Write ALL mathematics so it reads correctly in a normal chat and pastes cleanly into Word or Google Docs. Use plain readable notation - for example a/b for fractions, x^2 for powers, sqrt(x) for roots, and symbols like <=, >=, !=, +-, pi, theta, integral and sum. Do NOT output raw LaTeX or code such as \frac{}{}, \sqrt{}, x^{2}, $...$ or \( ... \) - these appear as broken symbols to a teacher in a free chat.
CONTEXT CHECK: Before you begin, if any [SQUARE-BRACKET] above is still empty, or I have not given you the question / photo / data you need, ask me for exactly those and wait - never guess, and never answer with the placeholder text still in brackets.
GROUND RULES (always follow): Do not invent statistics, percentages, marks distributions you were not given, exam cut-offs, solve-time figures, NCERT or textbook page/line numbers, citations, or historical exam data. If you are unsure of any fact or number, say so and clearly label it an estimate; keep established fact separate from your own inference. Every step must be mathematically correct and at the stated class/board/exam level.
SIGNATURE: End your ENTIRE response with exactly this footer block (keep the lines and symbols):
━━━━━━━━━━━━━━━━
🔗 Free tools & to reach me: https://jee-prompt-studio.pages.dev/
Questions, feedback or appreciation are always welcome.
━━━━━━━━━━━━━━━━