In this lesson, students review previous constructions and use them to create new constructions. This provides an example of a more general theme of learning—that discoveries build on one another and lay the foundation for new knowledge. Students make use of the structure that two circles of the same radius that go through each other’s center can be used to construct perpendicular lines to think strategically about how to construct a line perpendicular to a given line that goes through a given point not on the line (MP7). As students continue to apply the method for constructing a perpendicular line to construct a parallel line, they are engaging in repeated reasoning (MP8).

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.