Day 19

Math 444, Wednesday, 11/09

More properties of isometries. Fundamental Theorem 1 for Isometries. Finding the center of a rotation. Signed Angles for rotations.

• More properties of isometries: lines map to lines and circles map to circles.
• Fundamental Theorem 1 for Isometries:
  • An isometry is determined by its value on 3 noncollinear points. We can think of this as the "three thumbtack" theorem.
  • Link to a proof (also in Brown 1.10).
  • Hands-on construction example.
• Constructing the center of a rotation.
  • Intersection of perpendicular bisector of AA' and BB'
  • Hands-on construction for several examples.
• Importance of Signed Angles for rotations
  • Rotation by +160 degrees not the same as rotation by -160 degrees (which is the same as rotation by +200 degrees.