We used a task from Illustrative Mathematics as part of a performance assessment on Rigid Motions.
On the next page, △ABC has been reflected across a line into the blue triangle. Construct the line across which the triangle was reflected. Justify your conclusion.
Students used TI-Nspire to construct the line of reflection, and we asked them to explain their construction on paper. I monitored their work using Class Capture to see what approaches the students were using. This year, almost everyone created segments BB’ and CC’. Some also created segment AA’. Some then constructed the midpoint of the segments then created the line through those midpoints. Some used the perpendicular bisector tool. Our class discussion focused on what were the fewest number of objects we could construct to get the line of reflection.
And then I asked H.K. if she would share her work. She had the same idea as most of the others, but instead of drawing a segment with a vertex and its image as the endpoints (AA’, BB’, or CC’), she constructed the midpoint of segment BC and the corresponding midpoint of segment B’C’. Then she joined those image and pre-image points with the segment tool (actually vector tool) and constructed the perpendicular bisector of the segment. That’s a big deal. H.K. reminded us of an important property of rigid motions. Most of the segments and angles that we found congruent as we were exploring focused on the vertices of the triangle and their images. But the same is true from every point on the pre-image to its corresponding point on the image – not just from the vertices. Thanks for the reminder, H.K.
And so the journey continues ….