POLYGONS.

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Presentation transcript:

POLYGONS

WARM UP!!!

polygon not a polygon

What is 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”

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Polygon or Not a Polygon? Not Polygon because sides are not line segments.

Polygon or Not a Polygon?

Polygon or Not a Polygon? Not Polygon because sides are intersecting at more than the endpoints.

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Polygon or Not a Polygon? Not Polygon because sides are not intersecting at the endpoints.

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Polygon or Not a Polygon?

Polygon or Not a Polygon? Not Polygon because sides are intersecting more than one other side at its endpoint.

Naming Polygons A B D C 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.

Polygons can be named by their 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 interior angles / vertex angles 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? Concave because a segment connecting points on the polygon that will lie in the exterior can be drawn.

Convex or Concave? Convex

Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

Convex or Concave? Convex

Convex or Concave? Concave A segment connecting points on the polygon will lie in the exterior.

Concepts EQUIANGULAR POLYGON EQUILATERAL POLYGON REGULAR POLYGON

┌ ┌ ┌ ┌ ┌ ┌ ┌ ┌ EQUILATERAL but not EQUIANGULAR EQUILATERAL and EQUIANGULAR ┌ ┌ ┌ ┌ EQUILATERAL and EQUIANGULAR EQUIANGULAR but not EQUILATERAL ┌ ┌ ┌ ┌

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.

Practice Exercise Set 6.1 on pages 280-282 #1-6, 9-12, 18, 19 B. C. D.

polygon not a polygon