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:

ANY REGULAR POLYGON:

Given the side:

STAR POLYGONS: