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GPS Alignment Course
WEEK 13: GEOMETRY – POLYGONS
Tessellation Restrictions
Can any triangle be used to make a tessellation? Can any quadrilateral be used to make a
tessellation? Can any polygon be used to make a tessellation? Why or why not?
Summarize your findings.
GPS
M6G1. Students will further develop their
understanding of plane figures.
a. Understand the meaning of line and
rotational symmetry.
As seen in Problem Exploration
In order to solve this problem, the students
will have to have an understanding of what
tessellate means - rotating about one point
such that there are no overlaps or gaps.!
M7G1. Students will construct plane
figures that meet given conditions. They
will also demonstrate understanding of
transformations.
b.! Demonstrate understanding of
translations, symmetry, dilations, rotations
and reflections.
!
M8G1. Students will analyze and use
characteristics and properties of geometric
figures.
c.! Use and apply the properties of triangles
and parallelograms.
!
To find out which polygons tessellate, the
student can use either GSP, an applet, or
cut out various shapes from paper to see
which ones tessellate by actually rotating
the shape about a given point.!Some
triangles tessellate through reflection, some
rotation.
Not all polygons tessellate and using what
is known about certain polygons can help
determine which do.
If a triangle is rotated about the midpoint
of one of the sides, then a parallelogram is
formed.
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GPS Alignment Course
Sum of Angles in a Polygon
What is the sum of the angles of a triangle? of a quadrilateral? of a pentagon? of a
hexagon? What is the sum of the angles in convex polygons in terms of the number of
sides?
GPS
M6G1. Students will further develop their
understanding of plane figures.
As seen in Problem Exploration
The definition of convex and nonconvex
polygons will need to be understood.! Then
various convex polygons will need to be
constructed.
M6A2. Students will consider relations
between varying quantities.
a. Analyze and describe patterns arising from
function rules, tables, and graphs.
Have the students create table with the
columns: Polygon, #of Sides, #of
Triangles, Sum of Degrees.!!The pattern can
be generalized to (n-2) *180.
M7A3. Students will understand relations and
functions.
a.!Graph coordinates in a plane.
b.!Represent, describe and analyze a
functional relation from a table, graph, and/or
formula.
The students create a table with the number of
sides of a polygon in one
column and the
corresponding angle sum in the other.! Plot
the points.! The relationship is linear and is
represented as y = 180x -360.
M8A3. Students will graph and analyze
graphs of linear equations.
b.! Graph equations of the form y = mx + b.
d. Determine the equation of a line given a
graph or data.
e.!Interpret the meaning of the slope and yintercept in a given situation.
Extending from the above description, the
students will need to determine that the
relationship is linear, and determine the
equation by finding the slope from 2 of the
points, and then the y-intercept.
M8G1. Students will analyze and use
characteristics and properties of geometric
figures.
c. Use and apply the properties of triangles
and parallelograms.
The!sum of angles of a triangle is 180 degrees
and the polygons that aren't triangles can be
broken into triangles.!Therefore, a
relationship between the number of sides of a
polygon can be generalized.
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