Chapter 11 Extending Geometry

1
Chapter 11Extending Geometry

• Section 11.1
• Transformations

2
Transformations

• A transformation is a change that may or may not
  affect a figures size or shape.
• Types of Transformations
• Reflection
• Rotation
• Translation
• Glide Reflection

3
Reflection

• A reflection is a flip over a line.
• The line is the perpendicular bisector of the
  lines that contain corresponding points of the
  original figure and its reflection.

4
Rotation

• A rotation is a turn (measured in degrees) around
  a fixed point.

5
Translation

• A translation is a slide along a directed segment
  (slide arrow).

6
Glide Reflection

• A transformation that involves a combination of
  of a translation followed by a reflection.

7
Isometry

• An isometry is a transformation that preserves
  distance and other characteristics between
  geometric figures.

8
Definition of Congruence, Using Transformations

• Two figures are congruent if and only if there
  exists a translation, rotation, reflection, or
  glide reflection that sets up a correspondence of
  one figure as the image of the other.

9
Symmetry

• Reflectional (Line) Symmetry
• Exists when a plane figure can be folded in
  half in such a way that each point in one half of
  the figure corresponds in a special way to a
  unique point in the other half of the figure.
  The line along which the figure can be folded is
  called the line of symmetry.
• Rotational Symmetry
• Exists when a figure can be rotated between 0 -
  180 around a fixed point (center of rotational
  symmetry) and coincide with its original
  position.