The great part about this is that, if all goes according to plan*, this is the perfect segue to what is coming next today. (*I am out of town and don't know how far the class got yesterday.) I want students to come up with the equation of the line shown (likely by finding the slope and noticing the y-intercept) and then check their equation using Desmos.
On to the main event. I wanted to tie triangles back to the linear and quadratic work we did earlier this semester so I made this handout. Students will begin by calculating the perimeter for all the triangles from family 1 (from our similar triangles work) and add a few more triangles to the list. They will look at the pattern of the results and hopefully notice that is is constant when the scale factor increases by 1 and a multiple of the previous pattern when the scale factor increases by more than one.
Next they will graph the results and determine a model which will allow them to answer some questions about larger triangles. You may notice that I am giving them a graph with the scale set up for them and the axes labeled. As we progress through the course, I will give them less and expect more.
On to area:
On Monday I will see how it all went. I do love how this connects linear, quadratic and similar triangles - like a spiral within the first spiral : )