I’ve blogged about the Illustrative Mathematics task Reflected Triangles before. I really like that it asks students to determine the line of reflection given the pre-image and image instead of determining the image given the pre-image and line of reflection.

△ABC has been reflected across a line into the blue triangle. Construct the line across which the triangle was reflected. Justify your conclusion.

How would you construct the line of reflection?

Work on your mathematical flexibility to come up with more than one way to construct the line of reflection.

I used Class Capture to monitor student work and selected some students to share their approach with the whole class.

Many students approached the task like Paris:

What can we learn about the relationship between the pre-image, image, and line of reflection from the additional line in Max’s diagram?

I’ve always used this task towards the end of our unit on Rigid Motions, but I am thinking about using it earlier in the unit next year. Maybe the task itself could be an #AskDontTell approach for students learning what we want them to learn about the relationship between the pre-image, image, and line of reflection. We will see next year, as the journey continues …

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