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.
The following two animations demonstrate rotations with center B. It rotates a geometric figure consisting of three points and two line segments:
Rotation of the Plane Counter-Clockwise
Rotation of the Plane Clockwise
1. Let there be a rotation of d degrees around center O. Let P be a point other than O. Select a d so that d ≥ 0. Find P' (i.e., the rotation of point P) using a transparency.
2. Let there be a rotation of d degrees around center O. Let P be a point other than O. Select a d so that d < 0. Find P' (i.e., the rotation of point P) using a transparency.
3. Which direction did the point P rotate when d ≥ 0?
4. Which direction did the point P rotate when d < 0?
5. Let L be a line, AB be a ray, CD be a segment, and ∠EFG be an angle, as shown. Let there be a rotation of d degrees around point O. Find the images of all figures when d ≥ 0.
6. Let AB be a segment of length 4 units and ∠CDE be an angle of size 45&geg;. Let there be a rotation by d degrees, where d > 0 , about O. Find the images of the given figures. Answer the questions that follow.
a. What is the length of the rotated segment Rotation(AB)?
b. What is the degree of the rotated angle Rotation(∠CDE)
7. Let L1 and L2 be parallel lines. Let there be a rotation by d degrees, where -360 < d < 260, about O. Is (L1)' || (L2)'' ?
8. Let L be a line and O be the center of rotation. Let there be a rotation by d degrees, where d ≠ 180° about O. Are the lines L and L' parallel?
Rotations require information about the center of rotation and the degree in which to rotate. Positive degrees of rotation move the figure in a counterclockwise direction. Negative degrees of rotation move the figure in a clockwise direction.
Basic Properties of Rotations:
(R1) A rotation maps a line to a line, a ray to a ray, a segment to a segment, and an angle to an angle.
(R2) A rotation preserves lengths of segments.
(R3) A rotation preserves degrees of angles.
When parallel lines are rotated, their images are also parallel. A line is only parallel to itself when rotated exactly 180°.
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