Geometry 12-5 Symmetry

Vocabulary Image – The result of moving all points of a figure according to a transformation Transformation – The rule that assigns to each point of a figure another point in the plane

Vocabulary Rigid Transformation, Isometry – The image is congruent to the original figure Nonrigid Transformation – A transformation that does not preserve the size and the shape

Translation Translation – An isometry where each point is moved by the same translation vector

Translation

Rotation Rotation – An isometry in which each point is moved by the same angle measure in the same direction along a circular path about a fixed point

Rotation Rotation with Patty Paper

Reflection Reflection – An isometry in which each point and its image are on opposite sides and the same distance from a fixed line

Reflection

Investigation Get your supplies Straight Edge Patty Paper

Investigation Draw a polygon and a line of reflection next to it on a piece of patty paper

Investigation Fold your patty paper along the line of reflection and create the reflected image of your polygon by tracing it

Investigation Draw segments connecting each vertex with its image point. What conclusion can you draw comparing the segments and the line of reflection

Investigation Conjecture The line of a reflection is the perpendicular bisector of every segment joining a point in the original figure with its image

Vocabulary Reflectional Symmetry – The property that a figure coincides with itself under a reflection (mirror symmetry) Line of Symmetry – The line of reflection of a figure having reflectional symmetry

Vocabulary Rotational Symmetry – The property that a figure coincides with itself under some rotation Point Symmetry – The property that a figure coincides with itself under a rotation of 180°

Vocabulary N-Fold Rotational Symmetry – When the angle of rotation can be expressed as 360/n, for a positive value of n

Sample Problems

Homework Pages 664 – – 12 (draw diagrams), 25 – 32, 58 – 60

Honors Homework Pages 664 – – 12 (draw diagrams), 25 – 32, 44, 45, 47, 58 – 60