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

Section 7.5

H.Geometry – Chapter 7 – Definition Sheet