POLYGONS

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



Not Polygonbecause sides are not line segments.



Not Polygonbecause sides are intersecting at more than the endpoints.



Polygon



Not Polygonbecause sides are not intersecting at the endpoints.



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 Polygons Concave 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?


Convex or Concave?

Convex

Convex or Concave?


EQUIANGULAR POLYGONEQUILATERAL POLYGONREGULAR POLYGON

Concepts

EQUILATERAL but not EQUIANGULAR

EQUILATERAL and EQUIANGULAR

EQUIANGULAR but not EQUILATERAL

EQUILATERAL and EQUIANGULAR

┌

┌

┌

┌

┌

┌

┌

┌

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

Documents

POLYGONS