The purpose of this lesson is to lay the foundation for understanding the perpendicular bisector of a segment as both a line perpendicular to a segment passing through its midpoint (by definition) and the set of points equidistant to the endpoints. The second fact will be proven in a subsequent unit.

This lesson continues the theme of asking how much can be learned without using numbers to measure distance, and it also builds on students’ understanding of angle and perpendicular from previous grades. Students look for and make use of structure when they think about where their classmates should stand during “Human Perpendicular Bisector” in order to be the same distance away from two given points (MP7). The more students that correctly place themselves, the more apparent the structure. Once students determine the structure, they record it as a conjecture. A conjecture is defined as a reasonable guess that students are trying to either prove or disprove.

If students have ready access to digital materials in class, they can choose to perform all construction activities with the GeoGebra Constructions Tool accessible in the Math Tools or available at https://im612.org/construction-tool.