Lesson 3: 3-3: Rotations

1. What must be true about the image of a triangle after a rotation about a point?
2. Why do you need to use a ruler when you draw the image of a given figure under a rotation?
3. What is the relationship between 90 degree rotations about the origin and 270 degree rotations about the origin?
4. Why do you think rotations of greater than 360 degrees are rarely used?

Center of Rotation
Angle of Rotation

G.CO.4
Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
G.CO.5
Given a geometric figure and a rotation, reflections, or translation, draw the transformed figure. Specify a sequence of transformations that will carry a given figure onto another.

A rotation is a congruence transformation that turns every point of a preimage through a specified angle and direction about a fixed point, called the center of rotation. The angle of rotation is the angle formed by a point on the preimage, the center of rotation, and the corresponding point on the rotated image.
Mathematically proficient students understand and use stated assumptions and definitions in constructing arguments. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.

Windmills convert the wind's energy into electricity through the rotation of turbine blades.

Students approaching grade level can be given practice problems in small groups to work with other students or directly with the teacher.
Students beyond grade level can make deeper connections by completing rotations 90 degrees clockwise and 270 degrees counterclockwise to make the connection between the two.

Formative Assessment

Textbook in class

Access online textbook and resources through class link.