9.7
Tessellations
9.7 - Tessellations
„ A tessellation or tiling is a repeating pattern
of figures that completely covers a plane
WITHOUT gaps or overlaps.
„
These can be created with translations,
rotations, and reflections.
9.7 – Tessellations in Art
9.7 – Tessellations in Nature
9.7 – Tessellations in Life
9.7 – Tessellations
„ Because shapes in a tessellation do not
overlap or leave gaps, the SUM of the
measures of the angles around any vertex
must be 360°.
9.7 – Tessellations
„ Determine whether a regular 18-sided figure
tessellates a plane.
A=
180(n – 2)
n
A=
180(18 – 2)
18
A = 160
9.7 – Tessellations
„ Can you tessellate a plane with an equilateral
triangle?
„
Explain……….
9.7 – Tessellations
„ Theorem:
„
EVERY triangle tessellates
9.7 – Tessellations
„ EVERY quadrilateral tessellates.
9.7 – Tessellations
„ We have 2 more symmetries in this chapter.
REMEMBER – there is line / reflective
symmetry and point / rotational symmetry.
„ Now we also have:
„
Translational
Symmetry
Glide Reflectional
Symmetry
Chapter 9 – Need to Know
„ Types of Isometries (4):
Reflection
Translation
Glide Reflection
Rotation
Chapter 9 – Need to Know
„ Types of Symmetries (4):
Reflectional
Translational
Glide Reflectional
Rotational