Geometry proof helper for two-column and paragraph proofs
Proofs are where geometry stops being about numbers. You know the triangles look congruent but not which theorem gets you there. Send the given, the prove statement and the diagram, and your agent plans the proof backwards from the goal, writes it as a two-column table with a reason for every line, and checks yours against it.
The prompt
- Help me with this geometry proof: [GIVEN, PROVE AND DIAGRAM]. My class is [CLASS] and we may use these theorems: [THEOREMS ALLOWED]. My attempt: [MY PROOF]. First explain the plan in 2–3 sentences, working backwards from what we need to prove. Then write the full proof as a [PROOF FORMAT], numbering each statement and giving the exact postulate, definition or theorem as the reason. Mark where each given is used. Check my attempt line by line and tell me which reasons are missing or wrong. End with a similar proof for me to try, with just the first two lines filled in.
What to change
- [GIVEN, PROVE AND DIAGRAM]: Type the given and prove statements, and attach a photo of the diagram (labels matter).
- [CLASS]: E.g. "high school Geometry", "Honors Geometry", "GCSE Higher".
- [THEOREMS ALLOWED]: E.g. "SSS, SAS, ASA, AAS, HL, CPCTC, vertical angles". Or "anything in chapter 4".
- [MY PROOF]: Paste or photograph your proof, or write "not started".
- [PROOF FORMAT]: "two-column proof", "paragraph proof" or "flow proof".
Example result
- Given and prove
- • Given: M is the midpoint of AB, and CM is perpendicular to AB.
- • Prove: AC ≅ BC
- The plan
- To prove two segments are congruent, show they are corresponding parts of congruent triangles. Triangles AMC and BMC share side CM, have equal halves of AB, and both have right angles at M. That is SAS, then CPCTC.
- Two-column proof
- • 1. M is the midpoint of AB | Given
- • 2. AM ≅ BM | Definition of midpoint
- • 3. CM ⊥ AB | Given
- • 4. ∠AMC and ∠BMC are right angles | Definition of perpendicular lines
- • 5. ∠AMC ≅ ∠BMC | All right angles are congruent
- • 6. CM ≅ CM | Reflexive property of congruence
- • 7. △AMC ≅ △BMC | SAS (steps 2, 5, 6)
- • 8. AC ≅ BC | CPCTC
- Where the givens are used
- • "Midpoint" gives the first pair of sides (step 2).
- • "Perpendicular" gives the included angle (steps 4–5).
- Your attempt
- • Step 4: you wrote "∠AMC = 90°" with no reason. Add "Definition of perpendicular lines".
- • Step 6: you used SSS, but you never showed AC ≅ BC (that is what you are proving). Using it is circular. SAS avoids this.
- • The order in SAS matters: the angle must be between the two sides. Here ∠AMC sits between AM and CM, so SAS is valid.
- Your turn
- Given: AB ∥ DC and AB ≅ DC in quadrilateral ABCD. Prove: △ABC ≅ △CDA.
- • 1. AB ∥ DC | Given
- • 2. AB ≅ DC | Given
- • Continue from step 3. Hint: look for alternate interior angles along diagonal AC.
How to do it with todo.is
- Copy the prompt and add the given, the prove statement, a photo of the diagram and your own attempt.
- Send it in todo.is or to your agent on WhatsApp or Telegram.
- You get the plan, a full proof with a reason on every line and corrections to your version.
- Finish the practice proof and send it back for a check. Ask "which other theorem could work here?" to learn alternatives.
Tips for a better result
- Mark the diagram first: tick marks for congruent sides, arcs for congruent angles. The congruence shortcut usually jumps out.
- Work backwards. Ask "what would I need to know to prove this?" until you reach the givens.
- Look for free facts: shared sides (reflexive property) and vertical angles appear in most triangle proofs.
- Never use what you are trying to prove as a reason. Your agent flags circular steps.
geometry proof helper: FAQ
- Can it read the diagram from my textbook? Yes, from a clear photo. Point labels must be readable; your agent lists the points and relationships it sees so you can confirm before it writes the proof.
- What is CPCTC? Corresponding Parts of Congruent Triangles are Congruent. Once two triangles are proved congruent, you can use it as the reason that their matching sides or angles are congruent.
- Why is SSA not a valid congruence rule? Two sides and a non-included angle can make two different triangles, so they do not guarantee congruence. The only exception is HL for right triangles.
- Can it do coordinate or circle proofs? Yes. For coordinate proofs it uses the distance, midpoint and slope formulas and checks the algebra; for circles it uses inscribed angle, tangent and chord theorems.
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