Name:______Period:______Date:______Geometry Module 1 – Topic C – Lesson 17 - Rotations
Notes for lesson 17
The purpose of lesson 17 is for students to identify the properties of rotation, use constructions to find the center of rotation, get familiar with notations for rotation and rotate 90 degrees clockwise and counter clock wise with the help of an index card.
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, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G-CO.12 Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc. Example 1. Students will need an index card to use as a measure of a right angle. A quick modification for this activity would be talking about rotation as a rigid motion, positive and negative angle of rotation and use transparency to see how rotation is done. (Corresponds to G8 Module 2-Rotations)
Example 3- Students have to construct perpendicular bisectors of segments to find the center of rotation. It would be helpful to have students write the steps on 3 by 5 index cards so they can use them for further reference. Name:______Period:______Date:______Name:______Period:______Date:______Lesson 17 – Rotations
Learning Targets : I can rotate a pre-image around a center of rotation for a give angle of rotation I can use constructions to find the center of rotations I can state the properties of rotation
Exercise 1 (Discussion):
1. You will need an index card. Label one corner of the index card as F. 2. You’re going to use the index card to rotate the given triangle 90o counterclockwise. 3. Place the corner of your index card on the point F, then line up the right side of the index card with segment and mark the edge to indicate the length of . Make a light line using the left side of the index card to show the direction of . 4. Then, turn the card 90o counter clockwise so that you can use the length of along to plot A’. 5. Repeat these steps for each vertex of the figure, labeling the new vertices as you find them. 6. Connect the 3 segments that form the sides of your rotated image.
Notation: Name:______Period:______Date:______
The capital R stands for ______
The C stands for ______
The stands for ______
When is positive, you turn ______.
When is negative, you turn ______.
: In words, this means ______
Finding the center of rotation:
Exercise 2
1. Draw a segment connecting points and .
2. Using a compass and straightedge, find the perpendicular bisector of this segment.
3. Draw a segment connecting points and .
4. Find the perpendicular bisector of this segment.
5. The point of intersection of the two perpendicular bisectors is the center of rotation. Label this point .
6. Draw and .
Justify your construction: Estimate the measures of angles and . Do the angles appear to have the same measure?
Basic properties of rotations: Name:______Period:______Date:______. When performing a rotation, the center point remains fixed. states exactly that— the rotation function with center point that moves everything else in the plane , leaves only the center point itself unmoved. . For every other point — every point in the plane moves the exact same degree arc along the circle defined by the center of rotation and the angle .
Properties preserved under a rotation from the pre-image to the image. 1. Distance (lengths of segments remain the same) 2. angle measures (remain the same) 3. parallelism (parallel lines remain parallel) 4. collinearity (points remain on the same lines) 5. orientation (lettering order remains the same)
Identifying a Rotation Image
A regular polygon has a center that is equidistant from its vertices. Segments that connect the center to the vertices divide the polygon into congruent triangles. We can use this fact to find rotation images of regular polygons.
Example 3. PENTA is a regular pentagon with center O. a) Name the image of E for a 72° rotation counterclockwise about O. b) Name the image of P for a 216° rotation clockwise about O. c) Name the image of AP for a 144° rotation counterclockwise about O.
Example 4
is a regular quadrilateral with center . Name:______Period:______Date:______
Name the image of for a 180º rotation counterclockwise about .______
Name the image of for a 270º rotation clockwise about .
Example 5
is a regular hexagon with center .
a. Name the image of for a 300º rotation counterclockwise about .
b. Name the image of for a 240º rotation clockwise about . Name:______Period:______Date:______Lesson 17 – Rotations
Classwork
Exercise 1 a) Construct the center of rotation and label it . b) Draw an angle of rotation. c) Estimate the angle of rotation: ______≈ ______˚
2. Point O is the center of regular pentagon JKLMN. Find the image of the given point or segment for the given rotation. (counterclockwise) a. r(144°, O)(K) b. r(72°, O)(N) c. r(216°, O)(ML) d. r(360°, O)(JN) e. r(288°, O)(JO)
Exercise 3 Name:______Period:______Date:______Construct the center of rotation and estimate the angle of rotation for each pair of figures below.
4. Point O is the center of regular hexagon ABCDEF. Find the image of the given point or segment for the given rotation. (counterclockwise) a. R(120°, O)(F) b. R(180°, O)(B) c. R(300°, O)(BC) d. R(360°, O)(FE) e. R(60°, O)(E) f. R(240°, O)(AB)
Lesson 17 – Rotations
Problem Set/Homework Name:______Period:______Date:______
1. Find the center of rotation for the following rotation. Estimate the angle of rotation, and write with proper notation.
2. Find the center of rotation for the following rotation. Estimate the angle of rotation, and write with proper notation.