Explore further the rotations that you worked with in class this morning, but this time with GSP. The file is at this link.
For this part, explore the GSP file concerning rotations and also line reflections. The goal is to discover and explain a relationship between the two kinds of isometries.
This is a much longer treatment of the same topic, written for a past year. You will not have time to do all this. Don't worry about it. It is a resource that may help, so work through as much of this as you have time for, all the time keeping the big picture in mind.
This is the link to Part 3. Notice that the gsp file for this link is an earlier version of the file from Part 2.
Big Fact 1. The composition NM of two line reflections M and N is a rotation if the mirror lines intersect and a translation if the lines are parallel. In the intersecting case, the center of rotation is the point of intersection and the angle of rotation is twice the angle from the first mirror line to the second. In the parallel case, the translation vector is perpendicular to the mirror lines and is twice the distance from the first mirror line to the second. The sense of the angle or direction is from the first line towards the second in both cases.
Consequence. Every rotation and every translation is a double line reflection. There is more than one such double reflection for any given rotation or translation.
Big Fact 2. (coming soon) All about Triple line reflections.