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POLYGONS
WARM UP!!!
polygon not a polygon
• A polygon is a plane figure.• A polygon is a closed region.• A polygon is formed by three or more
line segments as its sides.• Each side of a polygon intersects only
one segment at each of its endpoints.• poli “many angled”
What is a polygon?
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Polygon
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are not line segments.
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting at more than the endpoints.
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Polygon
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are not intersecting at the endpoints.
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Polygon
Polygon or Not a Polygon?
Polygon or Not a Polygon?
Not Polygonbecause sides are intersecting more than one other side at its endpoint.
Polygons are named by writing their consecutive vertices in order, such as ABCD or CDAB for the polygon above.
We cannot name the polygon as DBAC.
NAMING POLYGONS
BA
CD
Polygons can be named by their number of sides.
Number of Sides Name of Polygon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
11 undecagon
12 dodecagon
Connecting to Prior Knowledge•Think of words
beginning with the prefixes tri-, quad-, pent-, and oct-.
•Examples: triathlon, quadriplegic, pentameter, and octopus.
Regions in a Polygon
Parts of a Polygon
•sides▫consecutive sides
included angle▫nonconsecutive sides
•interior angles / vertex angles▫consecutive angles
included side▫nonconsecutive angles
•exterior angles
Interior Angles of Polygons
• In a triangle the sum of the interior angles =180o
•In a quadrilateral the sum of the interior angles =360o
USING WHAT YOU KNOW ABOUT TRIANGLES PROVE IT!!
Interior Angles of Polygons
•Now how about a pentagon?
•In a pentagon the sum of the interior angles =540o
Interior Angles of Polygons
• In any polygon, the sum of the interior angles is: 180 (sides – 2)
• NOTE: sides-2 is equal to the number of triangles you can form in the interior of the polygon!
• What is the sum of interior angles in a: Hexagon – 720o
Octagon - 1080o
Decagon - 1440o
ALL POLYGONS???
ALL POLYGONS!
How can these polygons be divided into two groups?
Convex PolygonsConcave Polygons
Polygon Convexity
A polygonal region is convex if any segment joining any two points of the polygon is part of the interior region.
If a polygon is not convex, then its is concave.
Convex or Concave?
Convex
Convex or Concave?
Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.
Convex or Concave?
Convex
Convex or Concave?
ConcaveA segment connecting points on the polygon will lie in the exterior.
Convex or Concave?
ConcaveA segment connecting points on the polygon will lie in the exterior.
Convex or Concave?
Convex
Convex or Concave?
ConcaveA segment connecting points on the polygon will lie in the exterior.
EQUIANGULAR POLYGONEQUILATERAL POLYGONREGULAR POLYGON
Concepts
EQUILATERAL but not EQUIANGULAR
EQUILATERAL and EQUIANGULAR
EQUIANGULAR but not EQUILATERAL
EQUILATERAL and EQUIANGULAR
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Regular vs. Irregular polygons
Which of these is a regular pentagon?
Regular vs. Irregular polygons
Regular polygons are equilateral and equiangular
Examples??? Square, regular pentagon, equilateral triangle
Counterexamples??? Kite, rhombus, trapezoid, parallelogram, isosceles triangle
Parts of a Polygon
•Diagonals▫A diagonal of a polygon is any segment
that joins two nonconsecutive vertices. Figure shows five-sided polygon QRSTU. Segments QS , SU , UR , RT and QT are the diagonals in this polygon.
PracticeExercise Set 6.1 on pages 280-282
#1-6, 9-12, 18, 19A. B.
C. D.
For this parallelogram BE 10 AB 14DC BD
For this rectangle AE 8 AB 7DC BD
0For this rhombus ABC 144ABE BAD BEC
0For this trapezoid ADC 80 AC = 12
BAD BCD BD =
polygon not a polygon
