Vocabulary. Term Page Definition Clarifying Example. center of dilation. composition of transformations. enlargement. glide reflection.

Transcription

1 CHAPTER 12 Vocabulary The table contains important vocabulary terms from Chapter 12. As you work through the chapter, fill in the page number, definition, and a clarifying example. center of dilation Term Page Definition Clarifying Example composition of transformations enlargement glide reflection isometry line of 260 Geometry

2 CHAPTER 12 Vocabulary The table contains important vocabulary terms from Chapter 12. As you work through the chapter, fill in the page number, definition, and a clarifying example. Term Page Definition Clarifying Example center of dilation 873 The intersection of the lines that connect each point of the image with the corresponding point of the preimage. center composition of transformations 848 One transformation followed by another. N'' M'' P'' M enlargement 873 A dilation with a scale factor greater than 1. N M' P N' v P' glide reflection 848 The composition of a translation and a reflection across a line parallel to the translation vector. First translate the preimage along v. v J K L K' L' J' Then reflect the image across line. isometry 824 A transformation that does not change the size or shape of a figure. Reflections, translations, and rotations are all examples of isometries. line of 856 A line that divides a plane figure into two congruent reflected halves. 260 Geometry

3 CHAPTER 12 VOCABULARY CONTINUED Term Page Definition Clarifying Example line reduction rotational tessellation translation 261 Geometry

4 CHAPTER 12 VOCABULARY CONTINUED Term Page Definition Clarifying Example line 856 A figure that can be reflected across a line so that the image coincides with the preimage. reduction 873 A dilation with a scale factor greater than 0 but less than 1. A B C A' B' C' P rotational 857 A figure that can be rotated about a point by an angle less than 360 so that the image coincides with the preimage has rotational Order of rotational : In the transformation of a figure such that the image coincides with the preimage, the image and preimage have. tessellation 863 A repeating pattern that completely covers a plane with no gaps or overlaps. translation 863 A figure has translation if it can be translated along a vector so that the image coincides with the preimage. 261 Geometry

5 CHAPTER 12 Chapter Review 12-1 Reflections Tell whether each transformation appears to be a reflection Copy each figure and the line of reflection. Draw the reflection of the figure across the line Geometry

6 CHAPTER 12 Chapter Review 12-1 Reflections Tell whether each transformation appears to be a reflection Yes, the image appears to be flipped across a line. No, the figure does not appear to be flipped. Copy each figure and the line of reflection. Draw the reflection of the figure across the line Geometry

7 CHAPTER 12 REVIEW CONTINUED Tell whether each formation appears to be a translation An interior decorator represents a mural on a wall with a rectangle with vertices (4, 1), (7, 1), (7, 5) and (4, 5). She decides to move the mural on the wall to a new location by translating along the vector 3, 2. Draw the mural in its final position. y x Rotations Tell whether the transformation appears to be a rotation Geometry

8 CHAPTER 12 REVIEW CONTINUED Tell whether each formation appears to be a translation No, the figure appears to have been flipped. Yes, the figure appears to slide. 7. An interior decorator represents a mural on a wall with a rectangle with vertices (4, 1), (7, 1), (7, 5) and (4, 5). She decides to move the mural on the wall to a new location by translating along the vector 3, 2. Draw the mural in its final position. y x Rotations Tell whether the transformation appears to be a rotation Yes, the figure appears to have turned around a point. No, the figure appears to have been flipped. 275 Geometry

9 CHAPTER 12 REVIEW CONTINUED Rotate each figure with the given vertices about the origin using the given angles of rotation. 10. A(1, 2), B(3, 2), C(4, 0), 11. A(2, 5), B(4, 2), C( 2, 0); 90 D(0, 0); Compositions of Transformations 12. Draw the result of the following composition of transformations. Translate RSTU along V and then reflect it across line k. R k U S v T 13. DEF with vertices D(3, 5), E(6, 1) and F(1, 3) is reflected across the y-axis and then its image is reflected across the x-axis. Describe a single transformation that moves the triangle from its starting position to its final position. 276 Geometry

10 CHAPTER 12 REVIEW CONTINUED Rotate each figure with the given vertices about the origin using the given angles of rotation. 10. A(1, 2), B(3, 2), C(4, 0), 11. A(2, 5), B(4, 2), C( 2, 0); 90 D(0, 0); 180 A( 1, 2), B( 3, 2), C( 4, 0), D(0, 0) A( 5, 2), B( 2, 4), C( 2, 0) 12-4 Compositions of Transformations 12. Draw the result of the following composition of transformations. Translate RSTU along V and then reflect it across line k. R k T" U S v U" S" R" T k R U S R' U' S' T T' 13. DEF with vertices D(3, 5), E(6, 1) and F(1, 3) is reflected across the y-axis and then its image is reflected across the x-axis. Describe a single transformation that moves the triangle from its starting position to its final position. The image has been rotated Geometry

11 CHAPTER 12 REVIEW CONTINUED 12-5 Symmetry Explain whether each figure has a line of. If so, copy the figure and draw all lines of Explain whether each figure has rotation. If so, give the angle of rotation and the order of the Geometry

12 CHAPTER 12 REVIEW CONTINUED 12-5 Symmetry Explain whether each figure has a line of. If so, copy the figure and draw all lines of no line of no line of Explain whether each figure has rotation. If so, give the angle of rotation and the order of the No rotational Yes, 180, order: 2 Yes, 90, order: Geometry

13 CHAPTER 12 REVIEW CONTINUED 12-6 Tessellations Copy the given figure and use it to create a tessellation Classify each tessellation as regular, semiregular, or neither Determine whether it is possible to tessellate a plane with regular hexagons. If so, draw the tessellation. If not, explain why. 278 Geometry

14 CHAPTER 12 REVIEW CONTINUED 12-6 Tessellations Copy the given figure and use it to create a tessellation Classify each tessellation as regular, semiregular, or neither semiregular neither semiregular 26. Determine whether it is possible to tessellate a plane with regular hexagons. If so, draw the tessellation. If not, explain why. 278 Geometry

15 CHAPTER 12 REVIEW CONTINUED 12-7 Dilations Tell whether each transformation appears to be a dilation Draw the image of the figure with the given vertices under a dilation with the given scale factor centered at the origin. 30. R(2, 3), S(3, 5) and T(5, 5); scale factor: 2 y x 31. A( 8, 6), B( 8, 4), C(1, 6), D(1, 4); Scale factor: 1 2 y x Geometry

16 CHAPTER 12 REVIEW CONTINUED 12-7 Dilations Tell whether each transformation appears to be a dilation Yes, the figures are similar, and the image is not turned or flipped. No, the figures are not similar in shape. No, the figure has been flipped. Draw the image of the figure with the given vertices under a dilation with the given scale factor centered at the origin. 30. R(2, 3), S(3, 5) and T(5, 5); scale factor: 2 y x 31. A( 8, 6), B( 8, 4), C(1, 6), D(1, 4); Scale factor: 1 2 y x Geometry

17 CHAPTER 12 Postulates and Theorems Theorem Theorem Theorem A composition of two isometries is an isometry. The composition of two reflections across two parallel lines is equivalent to a translation. The translation vector is perpendicular to the lines. The length of the translation vector is twice the distance between the lines. The composition of two reflections across two intersecting lines is equivalent to a rotation. The center of rotation is the intersection of the lines. The angle of rotation is twice the measure of the angle formed by the lines. Any translation or rotation is equivalent to a composition of two reflections. 280 Geometry

18 CHAPTER 12 Postulates and Theorems Theorem Theorem Theorem A composition of two isometries is an isometry. The composition of two reflections across two parallel lines is equivalent to a translation. The translation vector is perpendicular to the lines. The length of the translation vector is twice the distance between the lines. The composition of two reflections across two intersecting lines is equivalent to a rotation. The center of rotation is the intersection of the lines. The angle of rotation is twice the measure of the angle formed by the lines. Any translation or rotation is equivalent to a composition of two reflections. 280 Geometry

19 CHAPTER 12 Big Ideas Answer these questions to summarize the important concepts from Chapter 12 in your own words. 1. Describe an isometry and give three examples. 2. Describe the composition of two reflections across two parallel lines in terms of the vector. 3. Describe the composition of two reflections across two intersecting lines in terms of its center and angle. 4. Describe how a figure is dilated in terms of size and shape. For more review of Chapter 12: Complete the Chapter 12 Study Guide and Review on pages of your textbook. Complete the Ready to Go On quizzes on pages 855 and 881 of your textbook. 281 Geometry

20 CHAPTER 12 Big Ideas Answer these questions to summarize the important concepts from Chapter 12 in your own words. 1. Describe an isometry and give three examples. Answers will vary. An isometry is a transformation that does not change the shape or size of a figure. Reflections, translations and rotations are all isometries. 2. Describe the composition of two reflections across two parallel lines in terms of the vector. Answers may vary. The composition of two reflections across two parallel lines is equivalent to a translation. The translation vector is perpendicular to the lines. The length of the translation vector is twice the distance between the lines. 3. Describe the composition of two reflections across two intersecting lines in terms of its center and angle. Answers may vary. The composition of two reflections across two intersecting lines is equivalent to a rotation. The center of rotation is the intersection of the lines. The angle of rotation is twice the measure of the angle formed by the lines. 4. Describe how a figure is dilated in terms of size and shape. Answers may vary. A dilation is a transformation that changes size of a figure but not the shape. The image and the preimage of a figure under a dilation are similar. For more review of Chapter 12: Complete the Chapter 12 Study Guide and Review on pages of your textbook. Complete the Ready to Go On quizzes on pages 855 and 881 of your textbook. 281 Geometry