1. Verify experimentally the properties of dilations given by a center and a scale factor:
Your students may understand generally what the term similar means, but it can be very specific when it comes to geometry. For instance, while Tia and Tamera Mowry are very similar (you know, since they're identical twins and all), they aren't geometrically similar. How on earth could that be?
In geometry, similar objects are exactly the same shape, but not necessarily the same size. So one object could be smaller than a pea and another could be larger than Antarctica, but if they have the exact same shape, they're similar. How curious.
Still, the idea of being "exactly the same shape" is a little vague. How can we be sure that two objects of different sizes still have the same shape? That's where dilations, centers, and scale factors come in.