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 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 Cool-down, in which students will need to write their own rules for given transformations.
Learning Goals
Compare and contrast (using words and other representations) rigid transformations, similarity transformations, and those that are neither.
Student-Facing Goal
Let’s analyze transformations that produce congruent and similar figures.
Student-Facing Targets
I can determine whether a transformation produces congruent or similar images (or neither).
Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).
Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
