Extra, focused practice with complete two-column proofs. Every proof here is a complete proof that ends by proving two triangles similar — by AA Similarity, SSS Similarity, or SAS Similarity. There is no step past the similarity statement: once the two triangles are proved similar, the proof is done. Proofs run from 3 steps up to 7. 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 (a similarity statement placed before the ratios or angle pairs it rests on, 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. A row that was shown is not a row you earned, and the completion message says so.
These proofs are short — three or four lines — and every one ends at the similarity statement. 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 run longer — five to seven lines — because the ratios or angle measures have to be built before the similarity test can be used. Every proof still ends at the similarity statement; similarity proofs have no step past it. 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.
Triangle Similarity Proofs — Mr. J Geometry. All activities on this page run entirely in your browser.