UNIT 5
POLYGONS
POLYGONSPolygons 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 POLYGONSaccording to the number of sides
3 4 53 6
7 8 9 10
ANGLEStypes 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 90-degree 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:
http://vimeo.com/41125037
Given the circle that circumscribes it:
Another procedure:
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:
STAR POLYGONS: