This lesson builds on prior knowledge about congruence to reinforce the idea that the rigid motions translations, reflections, and rotations preserve distances and angles. These motions and the sequences of the motions, called rigid transformations, affect the entire plane, but students generally focus on a single figure and its image (the result of a transformation). Students also recall that two figures are congruent if there is a sequence of translations, rotations, and reflections that takes one figure onto the other. Students work on an isometric grid so that they are pushed toward needing precise definitions.

During this lesson, students focus on translations and reflections. While students may mention them, rotations do not get defined until a subsequent lesson. When students analyze an error about reflections, they are critiquing the reasoning of others and making their own viable arguments (MP3).

This lesson is the first place where students add entries to their reference charts. This resource will contain definitions, theorems, and assertions. Theorems are reserved for conjectures that students prove. Students will encounter their first theorem of this course in a later lesson. This means that some assertions, statements the students believe are true but have not proved, are not proved because they are axioms, while others are not proved because the proof is beyond the scope of this course. Refer to the Course Guide for more information.

At this point, students define the distance between a point and a line as the distance along the perpendicular. In a subsequent unit, students will prove that the shortest path between a point and a line is along the perpendicular.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.