H.Geometry – Chapter 7 – Definition Sheet Definition of: ______________________ ______________________ ______________________ - A ___________________________ mapping of points in a figure to points in a resulting figure - Manipulating an original figure to get a new figure - The original figure - The resulting figure - Notation: often indicated with primes (apostrophes) NOTE: _________________________ correspondence: - Each _________________point has exactly one __________ point - Each ___________ point comes from exactly one _____________ Section 7.1 (Part 1)
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H.Geometry Chapter 7 Definition Sheet - Mrs. Klopatek's ... · H.Geometry – Chapter 7 – Definition Sheet _____ _____ An arrangement of shapes that can completely cover the plane
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H.Geometry – Chapter 7 – Definition Sheet
___
Definition of:
______________________
______________________
______________________
- A ___________________________ mapping of points
in a figure to points in a resulting figure
- Manipulating an original figure to get a new figure - The original figure - The resulting figure
- Notation: often indicated with primes (apostrophes) NOTE: _________________________ correspondence:
- Each _________________point has exactly one __________ point
- Each ___________ point comes from exactly one _____________
Section 7.1 (Part 1)
H.Geometry – Chapter 7 – Definition Sheet
Some Types of
__________________________
_____________________________________
- Preimage and image are same size and same shape.
_____________________________________
- Preimage and image are same shape but different sizes
_____________________________________
- Preimage and image are different shapes but different sizes
Definition of
_________________________
- A transformation preserving both ______________ and ________________
- Preimage and image are always ____________________
- Also known as a ________________________________________ or
_________________________________
H.Geometry – Chapter 7 – Definition Sheet
Definition of _________________________
- When a figure undergoes an isometry and the resulting images coincides with the preimage. (“coincides” = ends up in exactly the same location and position) Recall: Four types of isometries: ___________________________ ____________________________ ___________________________ ____________________________
Types of Symmetry
_________________________ Symmetry
____________of Symmetry
REFLECTIONAL SYMMETRY AKA:
- A figure that can be _______________________ over a line such that the
resulting image coincides with the preimage. - The reflecting line used to get the coincidental figures - Cuts the figure into two congruent mirror images of each other. ___________ Symmetry , _____________Symmetry, ___________ Symmetry
Section 7.1 – Part 2
H.Geometry – Chapter 7 – Definition Sheet
_________________________
Symmetry
_________________________ Rotational Symmetry
____________ Symmetry
- A figure that can be ___________________ around a point such that the resulting image coincides with the preimage.
- Rotation must be less than 360 degrees. - Where n is the number of times the figure coincides when doing a full 360 degree rotation. - 2-Fold rotational Symmetry (Each point is rotated or reflected over a single
point.)
H.Geometry – Chapter 7 – Definition Sheet
____________________
Symmetry
_______________________ Vector
If a _______________ of figures can be ______________________ a given distance and a given direction in such a way that the image pattern coincides with the preimage pattern .
Identifies the distance and direction of the translational symmetry Example: bricks on wall, wall paper patterns
_________________________
symmetry
If a _______________ of figures can undergo a __________________________ in such a way that the image pattern coincides with the preimage pattern .
H.Geometry – Chapter 7 – Definition Sheet
Regular Polygon Symmetry
Theorem
A Regular Polygon with “n” sides has:
_____ reflectional symmetries
_____- fold rotational symmetries o The smallest angle of rotation for the rotational symmetry
is ___________
H.Geometry – Chapter 7 – Definition Sheet
_______________________
_______________________
An arrangement of shapes that can completely cover the plane without any gaps or overlaps.
_____________________
Tessellation
When a tiling uses congruent copies of exactly one shape Note: The sum of angles at each vertex must equal ________ Example: ___________________, __________________, Pattern Blocks
_____________________
Tessellation
A monohedral tiling using copies of a single _______________ polygon. There are only _______ regular tessellations. Which regular polygons tessellate?
_____________________
Tessellation
When the ____________________________________ of _______________ polygons (of one or more kinds) meet in the same order at each vertex of a tessellation. -RECALL: Sum of angles at each vertex must equal 360 degrees Naming semiregular tessellations – Based on number of sides in the reg. polygon
- Choose a vertex in the tessellation - List the number of sides of each polygon at that vertex
o Start with the smallest number of sides o Move clockwise or counter-clockwise around the vertex o Use decimal points as separators.
Section 7.4
H.Geometry – Chapter 7 – Definition Sheet
H.Geometry – Chapter 7 – Definition Sheet
___________________________ Tessellations
There are only ________ different tessellations. ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________ ________________________
__________________ Tilings
The set of the 3 regular tessellations and the 8 semiregular tessellations of regular polygons.
- Aka a 1-uniform tilings as all the vertices are identical
______________________
Tessellation
A tessellation of regular polygons, but the arrangements at each vertex is NOT the same. Ex: 2-uniform tiling – 2 different arrangements 3-uniform tiling – 3 different arrangements
H.Geometry – Chapter 7 – Definition Sheet
H.Geometry – Chapter 7 – Definition Sheet
Recall: Tessellations with polygons
_________________ Tessellations
The sum of the angles at one vertex in a tessellation must equal __________
Tessellations using congruent copies of the ____________ shape Examples: Regular tessellations, pattern blocks
INVESTIGATION:
- Which triangles tesselate?
- Which quadrilaterls tesselate?
- Which pentagons tesselate? -
Tessellating Triangles Conjecture
____________________________ will create a monohedral tessellation
Tessellating
_____________________ Conjecture
_____________________________ will create a monohedral tessellation