Extra, focused practice with complete two-column proofs. Every proof here first proves two triangles congruent by SSS, SAS, ASA, AAS, or HL, the longer ones go on to CPCTC, and the challenge proofs go one or two steps past CPCTC. Proofs run from 4 steps up to 9. Work one proof at a time: fill every blank — by choosing from a drop-down list, or by dragging statement and reason chips into the empty rows — then press Check Proof.
Two things to know about how checking works. First, order matters where the logic says it does: some lines of a proof can trade places and the proof is still correct, and the checker accepts those trades — but a line that uses a fact you have not established yet (CPCTC before the triangles are proved congruent, for example) will be marked wrong even if the statement and reason match each other. Second, a correct row turns green and locks; a wrong row earns a hint and another try. Shorter proofs give you 2 checks before a stuck row is filled in and marked as shown; longer proofs give you 3, and challenge proofs give you 4. A row that was shown is not a row you earned, and the completion message says so.
Short proofs that end at the congruence statement, gentlest first. The first proof is the on-ramp: its lists only offer reasons from that proof's own world. From the second proof on, the lists also include reasons that do not belong — part of the work is leaving those alone.
These proofs keep going after the triangles are proved congruent and finish with CPCTC — one or two steps of it. Nothing in this section goes past CPCTC; proofs that do live in Section 3. This section also has a Build the Whole Proof, where the table starts empty. You get 3 checks per proof before a stuck row is shown.
Every proof in this section goes at least one step past CPCTC: set up the parts, prove the triangles congruent, use CPCTC, and finish somewhere new — proving lines parallel, that a point is a midpoint, or that a segment bisects an angle. This section also has a Build the Whole Proof, where the table starts empty. You get 4 checks per proof before a stuck row is shown.
Triangle Congruence Proofs — Mr. J Geometry. All activities on this page run entirely in your browser.