Lesson 11: Defining Reflections
About this lesson
In previous grades, students have verified experimentally the properties of rotations, reflections, and translations. In this lesson, students build on these experiences and on their straightedge and compass constructions to rigorously define reflections as transformations that take every point of a figure to a point directly opposite to it on the other side of the line of reflection and the same distance from the line of reflection. In a previous lesson, students conjectured that the perpendicular bisector of a segment is the same as the set of points equidistant to the segment’s endpoints. This conjecture is used to motivate the definition of reflection. Students will use the definition of reflection to prove theorems in this unit and subsequent units. When students analyze an error about reflections, they are critiquing the reasoning of others and making their own viable arguments (MP3).
The Information Gap Activity might take longer than expected since it's the first one in the course, in which case, this lesson might span two days.
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.
Lesson overview
 11.1 Warmup: Which One Doesn’t Belong: Crossing the Line (5 minutes)
 11.2 Activity: Info Gap: What’s the Point: Reflections (20 minutes)

11.3 Activity: Triangle in the Mirror (15 minutes)
 Digital applet in this activity
 Includes "Are you Ready for More?" extension problem
 Lesson Synthesis
 11.4 Cooldown: What Went Wrong? Reflection (5 minutes)
Learning goals:
 Comprehend that the term "reflection" (in written and spoken language) requires specifying a line of reflection.
 Determine whether a figure is a reflection of another.
 Draw reflections of figures.
Learning goals (student facing):
 Let’s reflect some figures.
Learning targets (student facing):
 I can describe a reflection by specifying the line of reflection.
 I can draw reflections.
Required materials:
 Geometry toolkits
 Preprinted slips, cut from copies of the blackline master
Glossary:

reflection  A reflection is defined using a line. It takes a point to another point that is the same distance from the given line, is on the other side of the given line, and so that the segment from the original point to the image is perpendicular to the given line.
In the figure, \(A'\) is the image of \(A\) under the reflection across the line \(m\).  Access the complete Geometry Course glossary.
Standards:
 This lesson builds on the standards:CCSS.8.G.A.1MS.8.G.1MO.8.GM.A.1aMO.8.GM.A.1bCCSS.HSGCO.A.1MS.GCO.1MO.G.CO.A.1CCSS.HSGCO.D.12MS.GCO.12MO.G.CO.D.11
 This lesson builds towards the standards:CCSS.HSGCO.A.4MS.GCO.4MO.G.CO.A.4CCSS.HSGCO.C.10MS.GCO.10MO.G.CO.C.9CCSS.HSGCO.C.9MS.GCO.9MO.G.CO.C.8
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