Understand similarity in terms of similarity transformations

verify experimentally the properties of dilations given by a center and a scale factor.

given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.

know precise definitions of angle, circle, perpendicular line, parallel line and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

given a rectangle, parallelogram, trapezoid or regular polygon, describe the rotations and reflections that carry it onto itself.

develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

Understand similarity in terms of similarity transformations.

Understand similarity in terms of similarity transformations

Understand similarity in terms of similarity transformations.