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Tessellations
A tessellation, or tiling, is a repeating pattern
of figures that completely covers a plane,
without gaps or edges.
Because the figures in a tessellation do not overlap
or leave gaps, the sum of the measures of the angles
around the vertex must be 360.
If the angles around a vertex are all congruent,
then the measure of each angle must be a factor
of 360.
Which figures tessellate?
Use this formula to check….
180(n – 2)
a = -------------n
If a is a factor of 360, the figure will tessellate.
Does a triangle tessellate? (n = 3)
180(3 – 2)
a = -------------3
Does a square tessellate? (n = 4)
180(?? – 2)
a = -------------??
Does a pentagon tessellate? (n = 5)
180(?? – 2)
a = -------------??
Regular tessellations are made up of regular
polygons.
Semi-regular tessellations are made up of
two or more regular polygons.
Can you tessellate these figures?
135 135
135
135
135
135
135 135
Check out this “cool” website of tessellations!
http://www.coolmath.com/tesspag1.htm
Homework:
p. 670
5 - 10, 24 - 27