The purpose of this lesson is to develop a rigorous definition of rotation, building on what students know from previous courses. Students first focus on what information is important for defining a rotation and then determine properties of rotations by rotating segments to make isosceles triangles. Students attend to precision when they clarify what information they need to uniquely determine a given rotation (MP6).
Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.
- Comprehend that the term "rotation" (in written and spoken language) requires several descriptors including angle, center, and direction.
- Determine whether a figure is a rotation of another.
- Draw rotations of figures.
- Let’s rotate shapes precisely.
- I can describe a rotation by stating the center and angle of rotation.
- I can draw rotations.
A rotation has a center and a directed angle. It takes a point to another point on the circle through the original point with the given center. The 2 radii to the original point and the image make the given angle.
\(P'\) is the image of \(P\) after a counterclockwise rotation of \(t^\circ\) using the point \(O\) as the center.
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