Students are introduced to vocabulary and notation related to rigid motions (e.g., transformation, image, and map).
Students are introduced to transformations of the plane and learn that a rigid motion is a transformation that is distance preserving.
Students use transparencies to imitate a rigid motion that moves or maps one figure to another figure in the plane.
Students perform translations of figures along a specific vector. Students label the image of the figure using appropriate notation.
Students learn that a translation maps lines to lines, rays to rays, segments to segments, and angles to angles. Students learn that translations preserve lengths of segments and degrees of angles.
Students learn that when lines are translated they are either parallel to the given line, or the lines coincide.
Students learn that translations map parallel lines to parallel lines.
Students know the definition of reflection and perform reflections across a line using a transparency.
Students show that reflections share some of the same fundamental properties with translations (e.g., lines map to lines, angle and distance preserving motion, etc.). Students know that reflections map parallel lines to parallel lines.
Students know that for the reflection across a line L, then every point P, not on L, L is the b isector of the segment joining P to its reflected image P′.
Students know how to rotate a figure a given degree around a given center.
Students know that rotations move lines to lines, rays to rays, segments to segments, and angles to angles. Students know that rotations preserve lengths of segments and degrees of measures angles. Students know that rotations move parallel lines to parallel lines.
Students learn that a rotation of 180 degrees moves a point on the coordinate plane (a,b) to (-a, -b).
Students learn that a rotation of 180 degrees around a point, not on the line, produces a line parallel to the given line.