So, we were reviewing this morning in Geometry getting ready to finish up our circle unit. I was reminding the kiddos of the angle and arc relationships we have been discussing. I had been writing things like where x is an angle formed by the intersection of two chords and a and b are the measures of the intercepted arcs. However, today as I drew my diagram for it one of my students suggested I mark is as seen below.
I think I am delighted by this and will write it this way from now on. It feels to me that it is a more natural way to think about this relationship instead of having a coefficient of 2 or a coefficient of 1/2 that might not seem at all intuitive. I then drew the following
I’d love to hear from some other teachers about whether this seems at all like an improvement over the more standard way of writing these equations.
That’s all for now, just needed to get that off of my chest!