Definition+of+similarity


 * First Learning Cycle: ** goal is to define similarity and investigate dilations. The objectives we will concentrate on are:


 * 1) Students explore transformations which do not distort the shape of an object (discover relationship)
 * 2) Students explain the effect of dilation on lines (passing through the center of dilation or not) (discover relationship)
 * 3) Students explain why proportionality of sides and congruency of angles is a result of the definition of similarity and not the definition of similarity.(comprehension and communication, appreciation)
 * 4) Given a dilation, students locate the center and the scale factor (algorithmic skill)
 * 5) Students understand that every dilation is uniquely determined by its effect on any two points in the plane (discover relationship)
 * 6) Students explain why any two circles are similar (discover relationship)
 * 7) Students explain why any two parabolas are similar (discover relationship)