We shall say that two figures in the plane are similar whenever one is congruent to a dilate of the other. Therefore the two quadrilaterals are similar, since one is just an enlargement of the other. Any two circles are similar, if the two circles have the same radius. We simply take dilation by 1 to satisfy the definition. For the moment, we will study similar triangles, as illustrated below.
We can easily generate similar triangles by dilating a triangle with respect to one of its vertices or with respect to a point 0 not a vertex like shown below.
Figure 3.2 Process
of dilating a triangle
Let T be a triangle whose sides have lengths a, b, c respectively. If we dilate T by a factor of r, we obtain a triangle which we denote by rT. The lengths of its sides will be ra, rb, rc, as we saw in the preceding section. Note that r can be any positive number. For instance in Figure below we have drawn triangles T, 
T, and 2T.
T, and 2T.