Exploring proof building blocks as scaffolds for proving high school geometry theorems

The present study focused on tasks designed to include interactively interrelated proof blocks, and examined whether students used them to construct complete or partial proofs. Twenty 10th-grade students participated in the study, which was based on an activity consisting of theorems to prove concerning segments and circles: the proportion of two intersecting chords, the proportion of two secant lines and the proportion between the secant line and tangent lines. Initially, the participants were not asked to prove the presented geometric theorems. However, they subsequently used these theorems as a basis for constructing deductive proofs for new, related claims. The findings revealed that the specially designed activities provided to the students may assist them in making sense of the interrelationships between the blocks of proof.