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Reflection and Rotation Symmetry

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Page 1: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Reflection and Rotation Symmetry

Page 2: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Reflection-Symmetric FiguresA figure has symmetry if there is an isometry that maps the figure onto itself. If that isometry is a reflection, then the figure has reflection symmetry.

Page 3: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Activity 1:Lines of symmetry can cut through shapes that have reflection symmetry

Draw in lines of symmetry for each:

ACG none

Page 4: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Segment Theorem:Figures with reflection symmetry have their pre-images and images equal distances from the reflection mirror.

5 in

6 in

10 in

5

6

10

Page 5: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Circle Symmetry:

How many lines of symmetry does a circle have??

Infinite!

Page 6: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Symmetric Figures Theorem:

Any symmetric figure is congruent to its image

Page 7: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Rotation Symmetry:A figure has rotational symmetry if it’s congruent after a rotation of 180 degrees or less (greater than zero).

Find the degrees of roation by dividing 360 by number of points.

360/3 = 120

Page 8: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Order of Rotational SymmetryThe order of rotational symmetry that an object has is the number of times that it fits on to itself during a full rotation of 360 degrees.

Page 9: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

What is the order of rotational symmetry of the shape below?

Rotational Symmetry

Page 10: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

1

23

4

5

What is the order of rotational symmetry of the shape below?

Order 5

Rotational Symmetry

Page 11: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

What is the order of rotational symmetry of the shape below?

Rotational Symmetry

Page 12: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

1

2

3

4

5

What is the order of rotational symmetry of the shape below?

Order 6

Rotational Symmetry

6

Page 13: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Equilateral Triangle

An equilateral triangle has rotational symmetry of order ?

Regular Polygons

Page 14: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Equilateral Triangle

An equilateral triangle has rotational symmetry of order ?

Page 15: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Equilateral Triangle

An equilateral triangle has rotational symmetry of order ?

12

33

Page 16: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Square

A square has rotational symmetry of order ?

Square

Page 17: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Square

A square has rotational symmetry of order ?

Page 18: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Square

A square has rotational symmetry of order ?

12

3

4

4

Page 19: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Point SymmetryA figure also has point symmetry if it can be rotated 180 degrees. (If the figure looks the same upside down, then it has point symmetry.)

360/4 = 90 two rotation make 180

Page 20: Reflection and Rotation Symmetry Reflection-Symmetric Figures A figure has symmetry if there is an isometry that maps the figure onto itself. If that

Examples:Name the type(s) of symmetry each figure has.

Rotation of 120 reflection

Rotation and point

reflection

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Point Symmetry - St. Louis Public Schools...Point Symmetry •Rotating a figure that has point symmetry 180o should look the same. 3.1 Symmetry and Coordinate Graphs Point Symmetry

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Document6 - Andrew Glassner · 2014-04-24 · Andrew Gl s Notebook (a) (b) (c) in Figure 3c. Since the mirror lines runs vertically, we say it has vertical reflection symmetry, which

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Name Date Transformations Review for Test Geometry · Translation Reflection Rotation Dilation Some Other Vocabulary Symmetry, Line of Symmetry, Point Symmetry, Rotational Symmetry

Elad Walach PIRS partial intrinsic reflectional symmetry IRSA Intrinsinc reflection symmetry axes

Rs symmetry, rotation, translation, reflection - review

Symmetry Translation Rotation Reflection Slide rotation (S n )

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 Rotation Translation Reflection. Symmetry

SYMMETRY Help Code : 040 + REFLECTION

Levels in reflection: core reflection as a means to ... · tion (Figure 1) and the accompanying interventions (Figure 2). Readers interested in a more detailed discussion of the reflection

Line Symmetry › wordpress › wp... · symmetry. • One half of the shape is the mirror image of the other half. • The fold is called a line of symmetry or reflection. Shapes

THE GEOMETRY OF REFLECTION GROUPSpeople.mpim-bonn.mpg.de/geordie/mpg.pdfTHE GEOMETRY OF REFLECTION GROUPS GEORDIE WILLIAMSON 1. REFLECTION GROUPS Our ﬁrst encounter with symmetry

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Multiple Reflection Symmetry Detection via Linear-Directional Kernel Density Estimation

Symmetry Tomáš Suk. Symmetry in 3D Reflection symmetry – plane of symmetry Rotational symmetry – axis of symmetry, combination of more axes? Translational

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U2 L4 Symmetry Lesson.notebook - Hendrick … · U2 L4 Symmetry Lesson.notebook 1 October 23, 2017 Oct 54:54 PM U2 L4 Symmetry Oct 54:55 PM Line or Reflectional Symmetry A figure