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CCSS

Content Standards G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

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CCSS

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  1. Content Standards 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. Mathematical Practices 2 Reason abstractly and quantitatively. 5 Use appropriate tools strategically. CCSS

  2. SWBAT use mathematical vocabulary (key terms in geometry) IOT describe transformations in the coordinate plane. • SWBAT graph pre-images and images under reflection and rotation using a variety of tools IOT analyze the properties of transformations. Then/Now

  3. Concept

  4. Use a protractor to measure a 45° angle counterclockwise with as one side. Extend the other side to be longer than AR. Draw a Rotation Rotate quadrilateral RSTV45° counterclockwise about point A. • Draw a segment from point R to point A. • Locate point R' so that AR = AR'. • Repeat this process for points S, T, and V. • Connect the four points to form R'S'T'V'. Example 1

  5. Draw a Rotation Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A. Answer: Example 1

  6. Draw a Rotation Quadrilateral R'S'T'V' is the image of quadrilateral RSTV under a 45° counterclockwise rotation about point A. Answer: Example 1

  7. For the diagram, which description best identifies the rotation of triangle ABC around point Q? A. 20° clockwise B. 20° counterclockwise C. 90° clockwise D. 90° counterclockwise Example 1

  8. For the diagram, which description best identifies the rotation of triangle ABC around point Q? A. 20° clockwise B. 20° counterclockwise C. 90° clockwise D. 90° counterclockwise Example 1

  9. Concept

  10. Use a protractor to measure a 115° angle clockwise with as one side. Draw Use a compass to copy onto Name the segment Rotations in the Coordinate Plane Triangle DEF has vertices D(–2, –1), E(–1, 1), and F(1, –1). Graph ΔDEF and its image after a rotation of 115° clockwise about the point G(–4, –2). First, draw ΔDEF and plot point G. Draw a segment from point G to point D. Repeat with points E and F. Example 2

  11. Rotations in the Coordinate Plane Answer: Example 2

  12. Rotations in the Coordinate Plane Answer: ΔD'E'F' is the image of ΔDEF under a 115° clockwise rotation about point G. Example 2

  13. A.B. C. D. Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1). Example 2

  14. A.B. C. D. Triangle ABC has vertices A(1, –2), B(4, –6), and C(1, –6). Draw the image of ΔABC under a rotation of 70° counterclockwise about the point M(–1, –1). Example 2

  15. Rotations in the Coordinate Plane Hexagon DGJTSR is shown below. What is the image of point T after a 90 counterclockwise rotation about the origin? A (5, –3) B (–5, –3) C (–3, 5) D (3, –5) Example 3

  16. Rotations in the Coordinate Plane Read the Test Item You are given a graph of hexagon DGJTSR and asked to identify the coordinates of the image of point T after a 90° counterclockwise rotation about the origin. Solve the Test Item To find the coordinates of point T after a 90counterclockwise rotation about the origin, multiply the y-coordinate by –1 and then interchange the x- andy-coordinates. (x, y) → (–y, x) (5, 3) →(–3, 5) Answer: Example 3

  17. Rotations in the Coordinate Plane Read the Test Item You are given a graph of hexagon DGJTSR and asked to identify the coordinates of the image of point T after a 90° counterclockwise rotation about the origin. Solve the Test Item To find the coordinates of point T after a 90counterclockwise rotation about the origin, multiply the y-coordinate by –1 and then interchange the x- andy-coordinates. (x, y) → (–y, x) (5, 3) →(–3, 5) Answer: The answer is C, (–3, 5). Example 3

  18. Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin? A. (–5, –4) B. (–5, 4) C. (5, 4) D. (4, –5) Example 3

  19. Triangle PQR is shown below. What is the image of point Q after a 90° counterclockwise rotation about the origin? A. (–5, –4) B. (–5, 4) C. (5, 4) D. (4, –5) Example 3

  20. Content Standards G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. Mathematical Practices 4 Model with mathematics. 8 Look for and express regularity in repeated reasoning. CCSS

  21. You drew reflections and rotations of figures. • Identify line and rotational symmetries in two-dimensional figures. • Identify line and rotational symmetries in three-dimensional figures. Then/Now

  22. symmetry • line symmetry • line of symmetry • rotational symmetry • center of symmetry • order of symmetry • magnitude of symmetry • plane symmetry • axis symmetry Vocabulary

  23. Concept

  24. Identify Line Symmetry A. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: Example 1

  25. Identify Line Symmetry A. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: yes; 7 lines of symmetry Example 1

  26. Identify Line Symmetry B. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: Example 1

  27. Identify Line Symmetry B. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry, and state their number. Answer: no Example 1

  28. A. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 3 lines D. no Example 1

  29. A. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 3 lines D. no Example 1

  30. B. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 4 lines D. no Example 1

  31. B. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 4 lines D. no Example 1

  32. C. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 4 lines D. no Example 1

  33. C. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number. A. yes; 1 line B. yes; 2 lines C. yes; 4 lines D. no Example 1

  34. Concept

  35. Identify Rotational Symmetry A. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry. Answer: Example 2

  36. Identify Rotational Symmetry A. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry. Answer: Yes the star has order 5 rotatonal symmetry and magnitude 360 ÷ 5 = 72°. The center of the star is the center of rotation. Example 2

  37. Identify Rotational Symmetry B. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry. Answer: Example 2

  38. Identify Rotational Symmetry B. State whether the figure has rotational symmetry. Write yes or no. If so, locate the center of symmetry, and state the order and magnitude of symmetry. Answer: The propeller has order 3 rotational symmetry and magnitude 360 ÷ 3 = 120°. The center of the propeller is the center of rotation. Example 2

  39. A. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry. A. Yes, order 8 and magnitude 45° B. Yes, order 4 and magnitude 90° C. Yes, order 4 and magnitude 180° D. No, the figure does not have rotational symmetry. Example 2

  40. A. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry. A. Yes, order 8 and magnitude 45° B. Yes, order 4 and magnitude 90° C. Yes, order 4 and magnitude 180° D. No, the figure does not have rotational symmetry. Example 2

  41. C. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry. A. Yes, order 3 and magnitude 90° B. Yes, order 4 and magnitude 90° C. Yes, order 2 and magnitude 180° D. No, the figure does not have rotational symmetry. Example 2

  42. C. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry. A. Yes, order 3 and magnitude 90° B. Yes, order 4 and magnitude 90° C. Yes, order 2 and magnitude 180° D. No, the figure does not have rotational symmetry. Example 2

  43. Concept

  44. Three-Dimensional Symmetry A. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: Example 3

  45. Three-Dimensional Symmetry A. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: both plane and axis symmetry Example 3

  46. Three-Dimensional Symmetry B. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: Example 3

  47. Three-Dimensional Symmetry B. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: neither plane nor axis symmetry Example 3

  48. A. State whether the figure has plane symmetry, axis symmetry, both or neither. A. plane symmetry B. axis symmetry C. both D. neither Example 3

  49. A. State whether the figure has plane symmetry, axis symmetry, both or neither. A. plane symmetry B. axis symmetry C. both D. neither Example 3

  50. B. State whether the figure has plane symmetry, axis symmetry, both or neither. A. plane symmetry B. axis symmetry C. both D. neither Example 3

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