Lesson Goals Identify and use rotations in a plane Identify relationships between rotations in a plane ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

Reflection-Rotation Theorem If two lines intersect, then a reflection in the first line followed by a reflection in the second line is the same as a rotation about the point of intersection. B A m C B’ A’ B’’ A’’

then the angle of rotation is 2 x o. Reflection-Rotation Theorem If x o is the measure of the acute or right angle formed by the two lines, xoxo B A C B’ A’ B’’ A’’ 2xo2xo m

k m J K L J’ K’ L’ J” K” L” 45 o C 90 o clockwise rotation Angle of Rotation = 2 X angle of the lines

q p X Y Y’ X’ Y” X” 75 o 150 o clockwise rotation

Rotational Symmetry A figure that can be mapped onto itself by a rotation of 180 o or less. 90 o

Rotational Symmetry A figure that can be mapped onto itself by a rotation of 180 o or less. 120 o

Rotational Symmetry A figure that can be mapped onto itself by a rotation of 180 o or less. No rotational symmetry

What are the properties of a rotation? How are reflections and rotations related? What does it mean when a figure has rotational symmetry?

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