Transcript Slide 1

7-9 Tessellations
Warm Up
Problem of the Day
Lesson Presentation
Course 3
7-9 Tessellations
Warm Up
Identify each polygon.
1. polygon with 10 sides
decagon
2. polygon with 3 congruent sides
equilateral triangle
3. polygon with 4 congruent sides
and no right angles rhombus
Course 3
7-9 Tessellations
Problem of the Day
If each of the capital letters of the
alphabet is rotated 180° around its
center, which of them will look the
same? H, I, N, O, S, X, Z
Course 3
7-9 Tessellations
Learn to create tessellations.
Course 3
7-9 Tessellations
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Vocabulary
tessellation
regular tessellation
Course 3
7-9 Tessellations
Fascinating designs can be made by
repeating a figure or group of figures.
These designs are often used in art and
architecture.
A repeating pattern of plane figures
that completely covers a plane with no
gaps or overlaps is a tessellation.
Course 3
7-9 Tessellations
In a regular tessellation, a regular
polygon is repeated to fill a plane. The
angles at each vertex add to 360°, so
exactly three regular tessellations exist.
Course 3
7-9 Tessellations
Additional Example 1: Creating a Tessellation
Create a tessellation with quadrilateral
EFGH.
There must be a
copy of each angle
of quadrilateral
EFGH at every
vertex.
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7-9 Tessellations
Check It Out: Example 1
Create a tessellation with quadrilateral IJKL.
J
K
L
I
There must be a copy of each angle of
quadrilateral IJKL at every vertex.
Course 3
7-9 Tessellations
Additional Example 2: Creating a Tessellation by
Transforming a Polygon
Use rotations to create a tessellation
with the quadrilateral given below.
Step 1: Find the midpoint of a side.
Step 2: Make a new edge for half of the side.
Step 3: Rotate the new edge around the
midpoint to form the edge of the other half
of the side.
Step 4: Repeat with the other sides.
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7-9 Tessellations
Additional Example 2 Continued
Step 5: Use the figure to make a tessellation.
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7-9 Tessellations
Check It Out: Example 2
Use rotations to create a tessellation
with the quadrilateral given below.
Step 1: Find the midpoint of a side.
Step 2: Make a new edge for half of the side.
Step 3: Rotate the new edge around the
midpoint to form the edge of the other half
of the side.
Step 4: Repeat with the other sides.
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7-9 Tessellations
Check It Out: Example 2 Continued
Step 5: Use the figure to make a tessellation.
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7-9 Tessellations
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Lesson Quiz
1. Explain why a regular tessellation with regular
octagons is impossible.
Each angle measure in a regular octagon is
135° and 135° is not a factor of 360°
2. Can a semiregular tessellation be formed
using a regular 12-sided polygon and a
regular hexagon? Explain.
No; a regular 12-sided polygon has angles
that measure 150° and a regular hexagon has
angles that measure 120°. No combinations of
120° and 150° add to 360°
Course 3