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Terms in this set (49)
What are two other names that can be used for reflection symmetry?
line symmetry and mirror symmetry
What is a tessellation?
a repeating pattern of shapes with no gaps or overlap of shapes
What is another word for tessellation?
Tiling
Who is the mathematician who gave us tessellations?
MC. Escher
Is there a rotational symmetry of Order 1? Why or why not?
Not really- If a shape is rotated so that the rotated image is the same as the pre image only once, then the symmetry is not counted. This would mean that the image would have to rotate a full 360 degrees before it was the pre image- this does not count as the order
How many semi regular tessellations are there
8
How many lines of symmetry does a regular dodecagon have ?
it has 12 sides, so it has 12 lines of symmetry
What is the name given to the number of times that a figure matches itself in rotational symmetry?
Order
Define regular polygon
Length of all sides are equal and length of all angles are equal
What test can be used to determine if a figure has reflection symmetry?
fold test
Define semi-regular tessellation
a repeating pattern of 2 or more regular polygons with no gaps or overlaps
Name the types of symmetry
Reflection (line) symmetry
Rotational (turn) symmetry
Point (origin) symmetry
What is unique about all triangles and quadrilaterals?
they all tesselate
Name the regular polygons that tesselate
squares, equilateral triangles, regular hexagons
identify a letter of the alphabet that does not have reflection symmetry.
G
Not all shapes have lines of symmetry, or they may have several lines of symmetry. For example a triangle can have 3, or 1, or no lines of symmetry. Illustrate these 3 cases
equilateral - 3 lines
Isosceles - 1 line
Scalene - no lines
If a cookie were a perfect circle, how many lines of symmetry, if any, would it have?
infinite lines of symmetry
Point Symmetry is also the same as which rotational symmetry order?
Order 2
Draw and label the number of symmetries for an equilateral triangle
3 lines of reflection symmetry
3 points of rotational symmetry
When we divide a figure or object into two even matching halves, we say that the figure has...
reflection symmetry
or line symmetry
or mirror symmetry
If the only rotational symmetry of a figure is the 360 degree turn, what is the name given to the symmetry?
Trivial Symmetry
What is another name for point symmetry?
Origin Symmetry
How does one name a tessellation? You can draw a picture
Pick a vertex
Count the number of sides of each shapes surrounding the vertex
order the numbers from least to greatest
Identify a letter of the alphabet that has two rotation symmetries. Write the letter down, and illustrate the two rotations
N -> Z
N
tessellation
a repeating pattern of shapes with no gaps or overlaps
covering of a plane
"tile"
Regular polygons that make tessellations
equilateral triangle, the square, and the regular hexagon
A technique to determine if a figure tessellates
rotate a shape about the midpoints of its sides
any triangle and any quadrilateral (even concave) will...
tessellate
3 types of tessellations
Regular (3) - equilateral triangle, square, regular hexagon
Semi-Regular (8) - 2 or more regular polygons
Demi-Regular (many) - curves, animals, etc.
Symmetry
a rigid motion that gives an image that is the same shape as the original shape
Reflection symmetry
a type of rigid motion for a 2d shape. "line symmetry"
line of reflection
cutes the figure into two parts. Each part fits exactly onto the other if folded on the reflection line
example of reflections in nature
leaves, blades of grass, flower pedals, insects, humans
Rotation Symmetry
a kind of rigid motion for 2d figures. A shape has rotational symmetry if it can be rotated around a fixed point until it fits exactly on the space it originally occupied.
Order 1's nickname
Trivial
Every shape has 360 degree rotational symmetry, but it is only counted if and only if there are other rotational symmetries
Center
the fixed turning point in rotational symmetry
In an isosceles triangle, the two angles opposite the sides of equal length must have equal measures bc of ...
Reflection symmetry
Reflection symmetry nicknames
line symmetry , mirror image symmetry
2d rotates about a
point
3d rotates about a
line
A regular tessellation is a pattern made by repeating a
regular polygon
regular tessellations names
triangles - 3,3,3,3,3,3
squares- 4,4,4,4
hexagons - 6,6,6
*to name, look at the vertex, and find how many shapes meet there
*the pattern is identical at each vertex!
Quadrilaterals lines of symmetry
square - 4
rectangle - 2
irregular - none
kite - 1
rhombus - 2
regular polygons have N number of lines of symmetry
however many sides it has
quadrilaterals - 4
pentagon - 5
A regular polygon of "n" sides has ____
"n" lines of symmetry
Point symmetry
when every part has a matching part
the same distance from the origin but in the opposite direction
*same as rotational symmetry of Order 2
Syn + metron
together and measure
symmetry
Reflection symmetry
the simplest symmetry
has a line of symmetry
can be any direction
image and pre image
transformation maps a pre image onto an image
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