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.