The goal of the lesson is for students to describe transformations in the coordinate plane, with a focus on identifying transformations as producing congruent or similar figures (or neither).
Students begin by using similar triangles to connect the coordinate rule \((x,y)\rightarrow (3x,3y)\) to the geometric definition of a dilation. Students have the opportunity to notice and make use of structure (MP7) when they compare 2 triangles and draw a conclusion about the proportionality of all the pairs of corresponding sides. Next, students match transformation rules to graphs, then explain which of these transformations are taking figures to similar or congruent figures. This builds toward the next activity and the cooldown in which students will need to write their own rules for given transformations.
The focus on congruence via equal distances throughout this lesson prepares students for subsequent activities that use distance to write equations for circles and parabolas.
Lesson overview
 3.1 Warmup: Why is it a Dilation? (10 minutes)

3.2 Activity: Congruent, Similar, Neither? (10 minutes)
 Includes "Are you Ready for More?" extension problem
 3.3 Activity: You Write the Rules (15 minutes)
 Lesson Synthesis
 3.4 Cooldown: Write a Rule (5 minutes)
Learning goals:
 Compare and contrast (using words and other representations) rigid transformations, similarity transformations, and those that are neither.
Learning goals (student facing):
 Let’s analyze transformations that produce congruent and similar figures.
Learning targets (student facing):
 I can determine whether a transformation produces congruent or similar images (or neither).
Standards:
 This lesson builds towards the standard(s): CCSS.HSGGPE.B.7MS.GGPE.7MO.G.GPE.B.6
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