Write a triangle proof worksheets

The congruence and similarity proof sheets hide one reason and let a child choose it; this is the next step, where the table is empty and the whole argument is theirs to write. A diagram, a Given, a Prove — and room to build the proof from nothing.

Kid stuck on one? You don’t just get the sheet.

Write a triangle proof
Write a triangle proof worksheet — Blank two-column proof to write, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

Choosing a reason from a bank is the on-ramp; writing the proof is the destination, and the two are meant to sit side by side — scaffold with one, assess with the other. Each figure here is one of the known-correct proofs the choice sheets use, so a teacher who has taught them recognises every one, but the child meets it as a blank two-column table with only the Given, the Prove, and the picture to start from.

Why this sheet works

This is a written worksheet, not an online exercise, for the same reason the puzzle sheets are: a proof has many valid orderings and wordings, so it cannot mark itself. The answer key is the model — every statement and the reason it rests on, written out in full — which is exactly what a child checks their own argument against.

How this one works

One question from this sheet, worked through a step at a time.

Prove △ABC ≅ △DEF

Prove:△ABC ≅ △DEF
1. ∠A ≅ ∠DGiven
2. ∠B ≅ ∠EGiven
3. BC ≅ EFGiven
4. △ABC ≅ △DEFAAS
  1. You are given ∠A ≅ ∠D; ∠B ≅ ∠E; BC ≅ EF, and you have to prove △ABC ≅ △DEF. Build it one line at a time — each line is a statement and the reason it is true.
  2. 1. ∠A ≅ ∠D — This fact is handed to you in the Given — nothing has to justify it.
  3. 2. ∠B ≅ ∠E — This fact is handed to you in the Given — nothing has to justify it.
  4. 3. BC ≅ EF — This fact is handed to you in the Given — nothing has to justify it.
  5. 4. △ABC ≅ △DEF — Two pairs of angles and a side not between them are equal: AAS.
  6. That is the whole proof: the last line, △ABC ≅ △DEF, follows by AAS.