07.03 Angles, Arcs, and Radii -Guided Notes

1. Define the following vocabulary terms in your own words:

Vocabulary Term:	Definition:
Radii
Dilation

Comparing Progress Han and Tyler are each completing the same set of tasks on an online homework site. Han is using his smartphone and Tyler is using his tablet computer. Their progress is indicated by the circular bars shown in the Image. The shaded arc represents the tasks that have been completed. When the full circumference of the circle is shaded, they will be finished with all the tasks. Han's progress Tyler's progress O Tyler says, "The are length on my progress bar measures 4.75 centimeters. The arc length on Han's progress bar measures 2.25 centimeters. So, I've completed more tasks than Han has."\fA Constant Ratio Diego and Lin are looking at 2 circles. Diego says, "It seems like for a given central angle, the arc length is proportional to the R radius. That is, the ratio I/r has the same value as the ratio L/R because they have the same central angle measure. Can we prove that this is true? Lin says, "The big circle is a dilation of the small circle. If k is the scale factor, then R =kr." Diego says, "The arc length is the small circle is I = 0/360*2ar. In the large circle, it's L =0/360*2xR. We can rewrite that as L = 0/360*2ark. So L = kl." Lin says, "Okay, from here I can show that 1/r and L/R are equivalent."\f0 90 180 degrees + 270 360 radians +