chapter 9.5 and 9.6 symmetry and dilations. symmetry a figure has symmetry if there exists a rigid...
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CHAPTER 9.5 AND 9.6Symmetry and Dilations
SYMMETRY
A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide reflection- that maps the figure onto itself.
CONCEPT
EXAMPLE 1 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 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 Identify Line Symmetry
C. 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; 5 lines of symmetry
EXAMPLE 1
A. yes; 1 line
B. yes; 2 lines
C. yes; 3 lines
D. no
A. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number.
EXAMPLE 1
A. yes; 1 line
B. yes; 2 lines
C. yes; 4 lines
D. no
B. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number.
EXAMPLE 1
A. yes; 1 line
B. yes; 2 lines
C. yes; 4 lines
D. no
C. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number.
CONCEPT
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.
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.
Identify Rotational Symmetry
C. 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.
CONCEPT
Three-Dimensional Symmetry
A. State whether the figure has plane symmetry, axis symmetry, both, or neither.
Answer: both plane and axis symmetry
EXAMPLE 3Three-Dimensional Symmetry
B. State whether the figure has plane symmetry, axis symmetry, both, or neither.
Answer: neither plane nor axis symmetry
A. plane symmetry
B. axis symmetry
C. both
D. neither
A. State whether the figure has plane symmetry, axis symmetry, both or neither.
A. plane symmetry
B. axis symmetry
C. both
D. neither
B. State whether the figure has plane symmetry, axis symmetry, both or neither.
DILATIONS
A dilation or scaling is a similarity transformation that enlarges or reduces a figure proportionally with respect to a center point and a scale factor
Enlargement
Reduction
CONCEPT
Dilations in the Coordinate Plane
Trapezoid EFGH has vertices E(–8, 4), F(–4,
8),
G(8, 4) and H(–4, –8). Graph the image of
EFGH after a dilation centered at the origin
with a scale factor of
DILATIONS
Triangle ABC has the coordinates A (2, 1), B (-1, 3), and C (-2, -2). Graph the image of triangle ABC after a dilation centered at the origin with a scale factor of 2.
SCALE FACTOR
Find the scale factor if AB = 9 and A’B’ = 3.
Find the scale factor if CD = 5 and C’D’ = 20.
Find the scale factor if XY = 8 and X’Y’ = 12.