Transcript Polygons and Tessellations

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Objective
Classify polygons and determine angle
measure of polygons
Vocabulary
Polygon
A simple closed figure in a plane formed by
three or more line segments
Vocabulary
Pentagon
A polygon having five sides
Vocabulary
Hexagon
A polygon having six sides
Vocabulary
Octagon
A polygon having eight sides
Vocabulary
Nonagon
A polygon having nine sides
Vocabulary
Decagon
A polygon having ten sides
Vocabulary
Regular polygon
A polygon that has all sides congruent and all
angles congruent
Vocabulary
Tessellation
A repetitive pattern of polygons that fit together
with no holes or gaps
Vocabulary
Polygon
A simple closed figure in a plane formed by
three or more line segments
Example 1 Classify Polygons
Example 2 Classify Polygons
Example 3 Angle Measures of a Polygon
Determine whether the figure is a polygon. If it is,
classify the polygon and state whether it is regular.
If it is not a polygon, explain why.
Answer:
Not a polygon
Has curved sides
Figure has curved sides
Does not meet the definition of a
polygon
1/3
Determine whether the figure is a polygon. If it is,
classify the polygon and state whether it is regular.
If it is not a polygon, explain why.
Answer: pentagon,
not regular because all sides are not congruent
1/3
Determine whether the figure is a polygon. If it is,
classify the polygon and state whether it is regular.
If it is not a polygon, explain why.
Answer:
Hexagon
Not regular
because sides are
not congruent
Has 6 sides
Sides are not congruent
2/3
Determine whether the figure is a polygon. If it is,
classify the polygon and state whether it is regular.
If it is not a polygon, explain why.
Answer: not a polygon
because sides overlap
2/3
ALGEBRA Find the measure of each angle of a regular
heptagon. Round to the nearest hundredth of a degree.
Draw a regular heptagon
1
2
3
4
5
1800  5
9000
Using only 1 vertex, draw a line
to each of the other vertexes
Count the triangles
Remember: The sum of the
angles of a triangle is 1800
Multiply number of triangles by
1800
3/3
ALGEBRA Find the measure of each angle of a regular
heptagon. Round to the nearest hundredth of a degree.
2
Count number of angles in
heptagon
3
1
4
7
6
Divide total degrees by number
of angles
5
9000
7
Answer: 128.570
3/3
Find the measure of each angle in a regular hexagon.
Answer: 120
3/3
Lesson 10:7
Assignment
Polygons
8 - 25 All
Using a protractor
Draw a triangle with one angle 1200 and two angles 300
Cut the triangle out and make 5
copies to make 6 triangles
Try to form a tessellation
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PATTERNS Ms. Pena is creating a pattern on her wall.
She wants to use triangles with angles 120, 30, and
30. Can Ms. Pena tessellate with these triangles?
The sum of the measures of the angles where the vertices
meet must be 360
Both 30 and 120 divide evenly into 360. Therefore,
Ms. Pena can arrange the triangles in a way that the
angles where the vertices meet make 360. She can
tessellate with these triangles.
4/4
Check
You can check if your answer is correct by drawing
a tessellation of triangles with angles measuring 120°, 30°,
and 30°.
Answer: Yes, they can be arranged in a way that the
angles where the vertices meet make 360.
4/4
*
QUILTING Emily is making a quilt using fabric pieces
shaped as equilateral triangles. Can Emily tessellate
the quilt with these fabric pieces?
Answer: Yes, they can be arranged in a way that the
angles where the vertices meet make 360.
4/4
Using a protractor
Draw a triangle with three angles 600 each
(equilateral triangle)
Cut the triangle out and make copies
to make as many triangles as you
need to form a tessellation
4/4