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Definition of Rotation and Basic Properties & Rotations of 180 Degrees - 8.2 - Lesson 5 & Lesson 6

Definition of Rotation and Basic Properties & Rotations of 180 Degrees - 8.2 - Lesson 5 & Lesson 6

Author: Todd Parks
Description:

Student Outcomes

  • 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.

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Tutorial

180 Degree Dunks

Here is a highlight reel of some of the greatest 180 degree slam dunks! Remember that 180 degree rotation is turning half way around.

What and How

We now have definitions for all three rigid motions:  translations, reflections, and rotations.

  • Rotations move lines to lines, rays to rays, segments to segments, angles to angles, and parallel lines to parallel lines, similar to translations and reflections.
  • Rotations preserve lengths of segments and degrees of measures of angles similar to translations and reflections.
  • Rotations require more than one piece of information (i.e., center of rotation and degree), whereas translations require only a vector, and reflections require only a line of reflection.

 

 

We now know that a 90 degree rotation will transform the object.

REMEMBER:  Rotating an object a positive amount of degrees is a counter-clockwise motion.

                        Rotating an object a negative amount of degrees is a clockwise motion.

Printable Blank Lesson 5

This is a printable blank version of Lesson 5 for Module 2 8th grade math.

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Rotating an Object 45 Degrees Using a Ruler and Protractor

We are now graduating from using tracing paper to view a rotation, and learning how to rotate a figure any amount of degrees by using a protractor and a ruler.

What and How - Rotating 180 Degrees

Rotations of degrees are special:

  • A point, P, that is rotated 180 degrees around a center O, produces a point P' so that P, O, P' are collinear.

(Collinear means that the points all can be connected with one straight line)

 

  • When we rotate around the origin of a coordinate system, we see that the point with coordinates  is moved to the point .
  • We now know that when a line is rotated  degrees around a point not on the line, it maps to a line parallel to the given line.

Printable Blank Lesson 6

This is a printable blank version of Lesson 6 in Module 2 for 8th grade.

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