POLYGONS

polygon not a polygon

• A polygon is a plane figure.• A polygon is a closed region.• A polygon is formed by three or more

segments as its sides.• Each side of a polygon intersects only

one segment at each of its endpoints.• poli + gonus “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 segments.

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Not Polygonbecause sides are intersecting not just 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 not just 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.

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

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.

ALL POLYGONS

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?

Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.

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?

Concavebecause a segment connecting points on the polygon that will lie in the exterior can be drawn.

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

Connecting to Prior Knowledge•Think of words

beginning with the prefixes tri-, quad-, pent-, and oct-.

•Examples: triathlon, quadriplegic, pentameter, and octopus.

•Meanings? (words and prefixes)

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

EQUIANGULAR POLYGONEQUILATERAL POLYGONREGULAR POLYGON

Concept Emphasis

EQUILATERAL but not EQUIANGULAR

EQUILATERAL and EQUIANGULAR

EQUIANGULAR but not EQUILATERAL

EQUILATERAL and EQUIANGULAR

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