Identify and describe symmetry in geometric figures Use transformations to draw tessellations Identify regular and semiregular tessellations

1. Obj. 33 Symmetry & Tessellation
The student is able to (I can):
• Identify and describe symmetry in geometric figures
• Use transformations to draw tessellations
• Identify regular and semiregular tessellations

2. symmetry
A figure can be transformed such that the
image coincides with the preimage.
Line symmetry (or reflection symmetry)
Rotational symmetry

3. angle of
rotational
symmetry
The smallest angle through which a figure
can rotated to coincide with itself.
90º
•
60º
•

4. Examples
Tell whether each figure has line symmetry.
If so, how many lines are there?
1.
4 lines of
symmetry
2.
H
2 lines of symmetry
3.
No line
symmetry

5. Examples
Tell whether each figure has rotational
symmetry. If so, give the angle of
rotational symmetry.
1.
Yes; 120º
2.
No rotational symmetry
3.
Yes, 45º

6. plane
symmetry
A plane can divide a three-dimensional
figure into two congruent reflected halves.
symmetry
about an axis
There is a line about which a threedimensional figure can be rotated so that
the image coincides with the preimage.

7. Examples
Tell whether each figure has plane
symmetry, symmetry about an axis, or
both.
1.
Both
2.
Plane symmetry

8. tessellation
A repeating pattern that completely covers
a plane with no gaps or overlaps.
Note: The measures of the angles that
meet at each vertex must add up to 360º.
Because the angle measures of any
quadrilateral add to 360º, any
quadrilateral can be used to tessellate.

9. regular
tessellation
A tessellation formed by congruent regular
polygons. The only regular polygons that
will tesselate are triangles,
squares, and hexagons.
semiregular
tessellation
A tessellation formed by two or more
different regular polygons with the same
number of each polygon occurring in the
same order at every vertex.

10. Examples
Classify the tessellations as regular,
semiregular, or neither.
1.
A hexagon meets two
squares and a triangle
at each vertex. It is
semiregular.
2.
Only hexagons
are used. It is
regular.
3.
It is neither regular
nor semiregular.