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UNIT 5
POLYGONS
POLYGONS
Polygons are many-sided figures,
with sides that are line segments.
The word polygon is a
combination of two Greek
words: "poly" means many
and "gon" means angle.
Polygons are named according
to the number of sides and
angles they have.
A regular polygon is one that
has equal sides and angles.
Polygons also have diagonals,
which are segments that join
two vertices and are not
sides.
POLYGONS IN NATURE
POLYGONS IN ART AND ARCHITECTURE
http://www.dartmouth.edu/~matc/math5.geometry/unit5/unit5.html
POLYGONS IN ART AND ARCHITECTURE
http://www.msdgeometry.com/joomla/index.php?option=com_hwdphotoshare&task=viewphoto&photo_id=5&Itemid=155
CLASSIFICATION OF POLYGONS
according to the number of sides
3
4
5
6
7
8
9
10
ANGLES
types of angles
ACUTE ANGLE: < 90º
RIGHT ANGLE: = 90º
OBTUSE ANGLE: > 90º < 180º
STRAIGHT ANGLE: =180º
TRIANGLES: classification by their angles
TRIANGLES: classification by their sides
QUADRILATERALS:
A QUADRILATERAL is a four-sided polygon with four
angles. There are many kinds of quadrilaterals.
PARALLELOGRAM: A quadrilateral with opposite sides
parallel.
NON PARALLELOGRAM: A quadrilateral with two
sides parallel or no sides parallel.
QUADRILATERALS:
PARALLELOGRAM: Quadrilaterals with opposite sides parallel.
square:
quadrilateral with
four equal sides and
four 90 degree
angles.
rectangle:
quadrilateral
with four 90degree
angles.
rhombus:
parallelogram
with four equal
sides.
rhomboid:
parallelogram
with opposite
sides equal
and parallel.
QUADRILATERALS:
NON PARALLELOGRAM: A quadrilateral with two sides
parallel or no sides parallel.
Trapezium: quadrilateral with two sides
parallel.
Trapezoid: quadrilateral with no sides parallel.
REGULAR POLYGONS: A regular polygon
has equal angles and sides. Regular polygons can be inscribed
in circles.
Elements of a Regular Polygon
- Center: The center is the inner point
equidistant from each vertex.
- Radius: The radius, r, is the segment that
goes from the center to each vertex.
- Apothem: The apothem, a, is the distance
from the center to the midpoint of one side.
REGULAR POLYGONS: A regular polygon
has equal angles and sides. Regular polygons can be inscribed
in circles.
EQUILATERAL TRIANGLE:
Given the side:
Given the circle that
circumscribes it:
Another procedure: http://vimeo.com/41125037
SQUARE:
Given the side:
Given the circle that
circumscribes it:
REGULAR HEXAGON:
Given the side or the circumference that circumscribes it:
REGULAR OCTAGON:
Given the side:
Given the circle that
circumscribes it:
REGULAR PENTAGON:
Given the side
Given the circle that
circumscribes it:
REGULAR HEPTAGON:
Given the side
Given the circle that
circumscribes it:
ANY REGULAR POLYGON:
Given the circle that circumscribes it:
ANY REGULAR POLYGON:
Given the side:
STAR POLYGONS: