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