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CPCTC proofs worksheets

CPCTC is the line that comes after a congruence proof: once the triangles are congruent, every matching pair of sides and angles is equal, including pairs nobody handed you. These free printable worksheets give the diagram, the Given and the Prove, and a two-column proof with one reason hidden.

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CPCTC proofs
CPCTC proofs worksheet — CPCTC after SSS, SAS, ASA, free printable with answer key

The answer key prints on a separate page.

What's on this sheet

A congruence proof stops at the criterion — SSS, SAS, ASA. This one goes a line further. The Prove is a pair of PARTS (∠B ≅ ∠D, or AD ≅ CD), the proof establishes the whole triangles first, and the last statement claims the part by CPCTC: corresponding parts of congruent triangles are congruent. Meeting it that way is the point. Taught in the same breath as SSS and SAS it sounds like a fifth criterion, which is the confusion it causes; taught as the step AFTER a proof, it is obvious.

Why this sheet works

Two rows are worth hiding and the sheets hide both. Naming the criterion means reading the tick marks and arcs; naming CPCTC means noticing that a statement claims something the Given never mentioned. The second is the harder of the two and the one the standard is about, so the reason bank always carries CPCTC whether it is the answer or not — a bank that only offered it when it was right would give the game away.

How this one works

Which reason completes the proof?

Step 4:△PTQ ≅ △RTS
△PTQ ≅ △RTS→SAS
SAS
  1. The proof is missing the reason for step 4: "△PTQ ≅ △RTS". Read what that step claims.
  2. Two pairs of sides and the angle between them are equal: SAS.
  3. So the missing reason is SAS.

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