The construction of a dilation is closely related to the "eyeball test" for similarity: Hold up two plane figures in parallel planes, close one eye, and move the figures until they align exactly or you know that they can't.

The first graphics view shows a large triangle, ABC. [br]The 3D graphics view shows the eyeball test with a smaller, similar triangle, A'B'C'. Lines of sight show A and A' lined up with the eye; the same holds for B and B and C and C'.[br]By clicking the check boxes in the first graphics view, you can see a parallel projection of this 3D figure into the plane of ABC. The flattened pictures is the projection, which is also the dilation construction.[br]The third checkbox, Show plane EAB, shows this plane in the 3D window. The right hand graphics view shows this plane in 2 dimensions.[br][br]For you to do: use Euclid's definition of similar polygons (corresponding angles equal, corresponding sides proportional) to prove that[br](a) a dilation produces a similar figure and[br](b) the eyeball test really does determine similar figures.