2 They are c - Oakland Schools Moodle

Back to Lesson 6-3
Name
Name
6-2B
page 2
PROPERTIES
Objective E: Determine reflection and rotation
6-3A Lesson Master
Questions on SPUR Objectives
See pages 424–427 for objectives.
SKILLS Objective B
symmetries of a figure.
You will need a protractor and a ruler to complete these questions.
2
7. How many lines of symmetry does a rhombus that is not a square have?
1. a. First rotate P 90˚around Q. Label this image P'.
In 8−13, draw all lines of symmetry for each figure.
8.
9.
b. Then rotate P –90˚ around Q. Label this image P*.
10.
c. What is true about P', Q, and P*?
They are collinear.
1
1
11.
12.
13.
2
1
REPRESENTATIONS
2. Rotate PAL −150˚ around B.
Objective J: Translate and reflect figures on
a coordinate graph.
5
4
3
E
2
C⬘
a. Draw the reflection image over the x-axis.
C⬘
A
I⬘
1
B
P
x
−5
L
( 0, 4 )
C' =
( –4, 1 )
P
A⬘
T
I
b. Give the coordinates of the vertices of the image.
I' =
A
T⬘
C
E⬘
A⬘
1 2 3 4 5
−5 −4 −3 −2 −1
−1
−2
−3
−4
C
P⬘
L⬘
y
14. Graph the triangle with vertices I = (0, −4),
C = (−4, −1), and E = (−3, 3).
3. Rotate ACT 50˚ around P.
E' =
4. D'O'G' is the image of DOG after a rotation of 60˚
about A. Draw DOG.
( –3, –3 )
D
c. What is the relationship between the coordinates of the images
and preimages?
O
O⬘
The second coordinates are opposites.
G
D⬘
15. What is the reflection image of (1.3, –2.5)
(1.3, 2.5) b. over the y-axis? (−1.3, −2.5)
c. over the line x = 1.3? (1.3, −2.5)
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Name
A
G⬘
a. over the x-axis?
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Name
6-3A
page 2
PROPERTIES
Objective E
6-3B Lesson Master
VOCABULARY
5. Determine the value of n, if possible, for the n-fold rotation symmetry
of each quadrilateral.
Figure
1. When does a figure have rotation symmetry?
when it coincides with its rotation image
n
not possible
2
2
not possible
2
4
Quadrilateral
Parallelogram
Rhombus
Trapezoid
Rectangle
Square
2. If a figure has rotation symmetry, what is the center of the rotation called?
the center of symmetry
3. What is n-fold rotation symmetry (n ≥ 2)?
If a figure has n-fold rotation symmetry
(n ≥ 2), n is the smallest number of
rotations of equal magnitude needed to
rotate the figure around its center of
symmetry to its original position.
6. For each regular polygon, give the measure of the smallest possible
turn for rotation symmetry and the value of n for n-fold rotation symmetry.
Copyright © Wright Group/McGraw-Hill
a.
c.
b.
SKILLS Objective B: Draw the rotation image of a point or figure.
4. Rotate point A 135° about B.
Measure of
smallest turn:
n:
72°
5
60°
6
A⬘
45°
8
B
A
5. Rotate pentagon BLAST 90° about B.
T
B B⬘
L⬘
T⬘
L
S
A
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A⬘
S⬘
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Back to Lesson 6-3
Name
Name
6-3B
page 2
PROPERTIES
Objective E: Determine reflection and rotation
6-4A Lesson Master
See pages 424–427 for objectives.
SKILLS Objective C
symmetries of a figure.
1. True or false.
In 6−11, a. determine n for the n-fold rotation symmetry of the figure
(n ≥ 2) if one exists. b. How many lines of symmetry does the figure have?
6.
Questions on SPUR Objectives
7.
a. A regular pentagon can be the fundamental region of a tessellation.
8.
b. A regular hexagon can be the fundamental region of a tessellation.
c. A regular octagon can be the fundamental region of a tessellation.
a.
2
2
b.
9.
a.
3
b.
3
10.
a.
8
b.
16
a.
false
true
false
2. Trace the quadrilateral at the right. Use at least eight copies of the
quadrilateral to make a tessellation.
none b. 1
Sample:
11.
a.
2
b.
2
5
a.
b.
5
12. Describe a figure that has rotation symmetry, but not reflection symmetry.
Sample: the capital letter S
13. Describe a figure that has reflection symmetry but not rotation symmetry.
Sample: the capital letter M
3. Trace the figure at the right and make a tessellation with at least
eight copies of the figure.
14. The figure at the right is part of a symmetric figure. The lines are
lines of symmetry.
Sample:
No
a. Does the figure as it appears now have rotation symmetry?
b. If the figure is completed with reflection images, does the
completed figure have rotation symmetry? If it is n-fold, what is n?
Yes; n = 2
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Name
6-4B Lesson Master
6-4B
SKILLS Objective C: Create tessellations of polygons.
9.
Sample:
10.
Sample:
In 1−6, determine whether the statement is true or false.
page 2
true
true
false
true
false
false
1. All triangles tessellate.
2. All quadrilaterals tessellate.
3. All pentagons tessellate.
4. All hexagons tessellate.
5. All heptagons tessellate.
6. All octagons tessellate.
7.
8.
Sample:
Sample:
REVIEW
Lessons 6-2 and 6-3, Objective E
11. Consider the fundamental regions in Questions 7−10.
a. If the region has n-fold rotation symmetry, what is n?
7. n = 2; 8. none; 9. n = 4; 10. none
Copyright © Wright Group/McGraw-Hill
In 7−10, trace the figure at the right. Use the figure to make a tessellation
with at least six copies of the figure.
b. If the region has reflection symmetry, how many lines of symmetry are there?
7. none; 8. one; 9. four; 10. one
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