First, students will look at the picture, the givens, and the prove statement. The possibility of using the knowledge that “corresponding parts of congruent triangles are congruent” (CPCTC) to find the final pair of congruent angles may or may not occur to them at this time. However, they will almost certainly suspect that the two triangles are congruent. In the toolkit of blocks before them, there are only four that have congruent triangles as an output. They separate those from the rest and then look at the given information: two pairs of congruent sides and a pair of congruent angles. These givens are appropriate inputs for only one of those four blocks: SAS Postulate.

Since the givens satisfy the three required inputs to SAS, students can see that they have completed the first part of the proof, and can now focus their attention on the second piece. The SAS Postulate proves that triangles are congruent, so they must now find a block in their toolkit that takes congruent triangles as an input. CPCTC fits that description and returns congruent segments or angles, the latter being the aim of the proof. Our students can now draw their proof as shown, certain that their logic is correct because all of the inputs and outputs of the blocks match. They know that they have reached the end because the final outgoing piece of information matches the prove statement in the original problem.

Consider how students might complete the very basic proof of congruent angles shown to the left. ProofBlocks allows students to start working in the middle of the proof instead of having to begin with only the givens.