EXERCISES
For more practice, see Extra Practice.
Practice and Problem Solving
A
Practice by Example
Example 1
(page 667)
Example 2
(page 668)
Example 3
(page 669)
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Does the picture show a tessellation of repeating figures? If so, identify a
transformation and the repeating figure.
1.
2.
3.
4.
Determine whether each figure will tessellate a plane.
5. equilateral triangle
6. square
7. regular pentagon
8. regular heptagon
9. regular octagon
List the symmetries in each tessellation.
11.
12.
13.
14.
15.
16.
Chapter 12 Transformations
10. regular nonagon
B
Apply Your Skills
Use each figure to create a tessellation on dot paper.
17.
18.
19.
Show how to tessellate with each figure described below. Try to draw
two different tessellations. If you think that two are not possible, explain.
20. a scalene triangle
21. the pentagon at the right
22. a quadrilateral with no sides parallel or congruent
23. Writing A pure tessellation is a tessellation made up of congruent copies of one
figure. Explain why there are three, and only three, pure tessellations that use
regular polygons. (Hint: See Exercises 5–10.)
Decide whether a semiregular tessellation (see photo) is possible using the given
pair of regular polygons. If so, draw a sketch.
24.
25.
Can each set of polygons be used to create a tessellation? If so, draw a sketch.
26.
27.
60°
A semiregular tessellation is
made from two or more
regular polygons.
C
Challenge
Copy the Venn diagram. Write each exercise
number in the correct region of the diagram.
28. scalene triangle
29. obtuse triangle
30. equilateral n
31. isosceles n
32. kite
33. rhombus
34. square
35. regular pentagon
36. regular hexagon
37. regular octagon
Regular
figures
Polygons
Figures that tessellate
38. On graph paper, draw quadrilateral ABCD with no two sides congruent.
Locate M, the midpoint of AB, and N, the midpoint of BC.
a. Draw the image of ABCD under a 1808 rotation about M.
b. Draw the image of ABCD under a 1808 rotation about N.
c. Draw the image of ABCD under the translation that maps D to B.
d. Make a conjecture about whether your quadrilateral tessellates, using the
pattern in parts (a)–(c). Justify your answer.
Lesson 12-6 Tessellations
670-673
39. List steps (like those in Exercise 38) that suggest a way to tessellate with any
scalene triangle. Then list a second set of steps that suggest another way.
Standardized Test Prep
Multiple Choice
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Online lesson quiz at
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Web Code: afa-1206
Short Response
Extended Response
40. Which figure will NOT tessellate a plane?
A.
B.
C.
D.
41. You can tessellate a plane using a regular octagon together with which
other type of regular polygon?
F. triangle
G. square
H. pentagon
I. hexagon
42. Which is NOT a symmetry for the tessellation?
A. line symmetry
B. translational symmetry
C. rotational symmetry
D. glide reflectional symmetry
43. Is it possible to tile a plane with regular pentagons? Justify your answer.
44. Unit squares form this tessellation. Tell whether
this tessellation has each type of symmetry
(line, point, rotational, translational, or glide
reflectional). Explain.
Mixed Review
Lesson 12-5
Lesson 11-5
Coordinate Geometry A figure has a vertex at (–2, 7). If the figure has the given
type of symmetry, state the coordinates of another vertex of the figure.
45. line symmetry about the x-axis
46. line symmetry about the y-axis
47. point symmetry about the origin
48. line symmetry about the line y = x
Write the standard equation of each circle.
49.
50.
y
4
4
᎐4
O
y
4
2
x
᎐4
O
2
x
51. the circle with center (–1, 0) and radius 3
Lesson 10-1
Use Euler’s Formula, F ± V ≠ E ± 2, to find the missing number.
52. Faces: j
Edges: 16
Vertices: 9
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Chapter 12 Transformations
53. Faces: 12
Edges: j
Vertices: 20
54. Faces: 7
Edges: 12
Vertices: j
A P int in Time
1500
1600
1700
1800
1900
2000
A
mosaic is a picture or design made by setting tiny pieces of glass, stone, or
other materials in clay or plaster. A mosaic may be a tessellation. Most mosaics,
however, do not have a repeating pattern of figures. Mosaics go back at least
6000 years to the Sumerians, who used tiles to both decorate and reinforce walls.
During 100 and 200 A.D., Roman architects used two million tiles to create the
magnificent mosaic of Dionysus in Germany. In the years 1941–1951 Mexican
artist Juan O’Gorman covered all four sides of a 10-story library in Mexico with
7.5 million stones—the largest mosaic ever. It depicts Mexico’s cultural history.
Take It to the NET For more information about
mosaics, go to www.PHSchool.com.
Web Code: afe-2032
Lesson 12-6 Tessellations
670-673