Post on 14-Jan-2016
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Reflection and Rotation Symmetry
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.
Activity 1:Lines of symmetry can cut through shapes that have reflection symmetry
Draw in lines of symmetry for each:
ACG none
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
Circle Symmetry:
How many lines of symmetry does a circle have??
Infinite!
Symmetric Figures Theorem:
Any symmetric figure is congruent to its image
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
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.
What is the order of rotational symmetry of the shape below?
Rotational Symmetry
1
23
4
5
What is the order of rotational symmetry of the shape below?
Order 5
Rotational Symmetry
What is the order of rotational symmetry of the shape below?
Rotational Symmetry
1
2
3
4
5
What is the order of rotational symmetry of the shape below?
Order 6
Rotational Symmetry
6
Equilateral Triangle
An equilateral triangle has rotational symmetry of order ?
Regular Polygons
Equilateral Triangle
An equilateral triangle has rotational symmetry of order ?
Equilateral Triangle
An equilateral triangle has rotational symmetry of order ?
12
33
Square
A square has rotational symmetry of order ?
Square
Square
A square has rotational symmetry of order ?
Square
A square has rotational symmetry of order ?
12
3
4
4
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
Examples:Name the type(s) of symmetry each figure has.
Rotation of 120 reflection
Rotation and point
reflection