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CHAPTER 9.5 AND 9.6 Symmetry and Dilations
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CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

Dec 22, 2015

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Page 1: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

CHAPTER 9.5 AND 9.6Symmetry and Dilations

Page 2: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

SYMMETRY

A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide reflection- that maps the figure onto itself.

Page 3: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

CONCEPT

Page 4: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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

Page 5: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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

Page 6: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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

Page 7: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 8: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 9: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 10: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

CONCEPT

Page 11: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 12: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 13: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 14: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

CONCEPT

Page 15: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

Three-Dimensional Symmetry

A. State whether the figure has plane symmetry, axis symmetry, both, or neither.

Answer: both plane and axis symmetry

Page 16: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

EXAMPLE 3Three-Dimensional Symmetry

B. State whether the figure has plane symmetry, axis symmetry, both, or neither.

Answer: neither plane nor axis symmetry

Page 17: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

A. plane symmetry

B. axis symmetry

C. both

D. neither

A. State whether the figure has plane symmetry, axis symmetry, both or neither.

Page 18: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

A. plane symmetry

B. axis symmetry

C. both

D. neither

B. State whether the figure has plane symmetry, axis symmetry, both or neither.

Page 19: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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

Page 20: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

CONCEPT

Page 21: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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

Page 22: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.

Page 23: CHAPTER 9.5 AND 9.6 Symmetry and Dilations. SYMMETRY  A figure has symmetry if there exists a rigid motion- reflection, translation, rotation, or glide.

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.