Holt Geometry

12-5 Symmetry12-5 Symmetry

Holt Geometry

I CANI CAN

•Identify line symmetry, rotational symmetry, and translational symmetry

•Name the pre-image and image points of a transformation

•Draw a line of symmetry for a given figure.

●Find the equation of a line of symmetry

Holt Geometry

12-5 Symmetry

transformationisometrypre-imageimage

Vocabulary

Holt Geometry

12-5 Symmetry

A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called amapping.

Examples of transformations are: translations, reflections, rotations, and dilations.

A transformation is an isometry if the size and shape ofthe figure stay the same.

Which of the transformations above are an isometry?

Translations, reflections, and rotations

A transformation is a change in the position, size, or shape of a figure or graph. It is sometimes called amapping.

Examples of transformations are: translations, reflections, rotations, and dilations.

Holt Geometry

12-5 Symmetry

Every transformation has a pre-image and an image.

• Pre-image is the original figure in the transformation (the “before”). Its points are labeled as usual.

• Image is the shape that results from the transformation (the “after”). The points are labeled with the same letters but with a ' (prime) symbol after each letter.

Holt Geometry

12-5 Symmetry

Example

A

B

C

Pre-Image

B'

A'

C'

Image

Holt Geometry

12-5 Symmetry

symmetryline symmetryline of symmetryrotational symmetry

Vocabulary

Holt Geometry

12-5 Symmetry

A figure has symmetry if there is a transformation of the figure such that the image coincides with the preimage.

Holt Geometry

12-5 Symmetry

Holt Geometry

12-5 Symmetry

Example 1A: Identifying line of symmetry

Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry.

yes; eight lines of symmetry

Holt Geometry

12-5 Symmetry

Example 1B: Identifying line of symmetry

no line symmetry

Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry.

Holt Geometry

12-5 Symmetry

Example 1C: Identifying line of symmetry

Yes; four lines of symmetry

Tell whether the figure has line symmetry. If so, copy the shape and draw all lines of symmetry.

Holt Geometry

12-5 Symmetry

Tell whether each figure has line symmetry. If so, copy the shape and draw all lines of symmetry.

Check It Out! Example 1

yes; two lines of symmetry

a.

b.

c.

yes; one line of symmetry

yes; one line of symmetry

Holt Geometry

12-5 Symmetry

Try examples 1 -4 on “Reflections and Symmetry” Handout.

Holt Geometry

12-5 Symmetry

Holt Geometry

12-5 Symmetry

The angle of rotational symmetry is the smallest angle through which a figure can be rotated to coincide with itself. The number of times the figure coincides with itself as it rotates through 360° is called the order of the rotational symmetry.

Angle of rotational symmetry: 90° Order: 4

Holt Geometry

12-5 Symmetry

Example 2: Identifying Rotational Symmetry

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry.

no rotational symmetry

yes; 180°; order: 2

yes; 90°;order: 4

A. B.

C.

Holt Geometry

12-5 Symmetry

Check It Out! Example 2

Tell whether each figure has rotational symmetry. If so, give the angle of rotational symmetry and the order of the symmetry.

yes; 120°; order: 3

yes; 180°; order: 2

no rotational symmetry

a. b. c.

Holt Geometry

12-5 Symmetry

Example 3B: Design Application

Line symmetry and rotational symmetry; angle of rotational symmetry: 90°; order: 4

Describe the symmetry of each icon. Copy each shape and draw any lines of symmetry. If there is rotational symmetry, give the angle and order.

Holt Geometry

12-5 Symmetry

Try examples 5 -8 on “Reflections and Symmetry” Handout.

Holt Geometry

12-5 SymmetryWriting Equations for Lines of Symmetry

Remember equations for horizontal lines:

y = 2 is horizontal line crossing y-axis at 2y = –4 is horizontal line crossing y-axis at 4

y=2

y =–4

Holt Geometry

12-5 SymmetryWriting Equations for Lines of Symmetry

Remember equations for vertical lines:

x = 2 is vertical line crossing x-axis at 2x = –4 is vertical line crossing x-axis at –4

x=2x =–4

Holt Geometry

12-5 SymmetryWriting Equations for Lines of Symmetry

Writing equations in form of y=mx + b

m is the slope (rise/run)

3

2

m =3 2

b = 3

Equation of line: y = 3x + 3 2

Holt Geometry

12-5 Symmetry

1.

“Symmetry Worksheet” Practice Problems

Equation for line of symmetry_________________

Holt Geometry

12-5 Symmetry

“Symmetry Worksheet” Practice Problems

Equation: ___________________

2.

Write the equation of the line of symmetry

Holt Geometry

12-5 Symmetry

“Symmetry Worksheet” Practice Problems

3.

Equation: ____________________________

Write the equation of the line of symmetry

Holt Geometry

12-5 Symmetry

Finish problems for homework