Rigid Motions – Which Reflection?

We added to our introductory lesson on Rigid Motions this year. Sometime last year, I read Which Reflection is Best by Andrew Shauver.

I wondered what students would say without measuring and before studying reflections in depth. So I asked.

And then I asked again, after students had the opportunity to use appropriate tools strategically (most used a ruler).

Not very many changed their minds from their first glance.

 

Next we talked.

BK offered his argument as to why he chose B over D:

When I put the edges of one end of the ruler on A and A’, the line of reflection didn’t go down the middle of the ruler on D, but it did on B.

 

Oh…so is there something significant about the line of reflection matching the middle of the ruler?

We made sense of the significance with the yellow-ish angles.

We developed the vocabulary as it arose, instead of having students write lists of definitions with no context (I cringe to think about how many of my former students suffered through writing geometry vocabulary each unit) – midpoint, bisector, distance from a point to a line, perpendicular bisector.

And we ultimately concluded that the line of reflection will be the perpendicular bisector of the segment that joins a pre-image point with its image.

What a great example of use appropriate tools strategically – BK was using his ruler both to measure distance and to measure for right angles. 

And so as the journey continues, I am thankful for students who are willing to share their thinking and for teachers like Andrew who are willing to share their lessons.