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##### POLYGONS

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**not a polygon**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**Polygon or Not a Polygon?**Not Polygon because sides are not line segments.**Polygon or Not a Polygon?**Not Polygon because sides are intersecting at more than the endpoints.**Polygon or Not a Polygon?**Polygon**Polygon or Not a Polygon?**Not Polygon because sides are not intersecting at the endpoints.**Polygon or Not a Polygon?**Polygon**Polygon or Not a Polygon?**Not Polygon because sides are intersecting more than one other side at its endpoint.**Naming Polygons**• 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. A B D C**Connecting to Prior Knowledge**• Think of words beginning with the prefixes tri-, quad-, pent-, and oct-. • Examples: triathlon, quadriplegic, pentameter, and octopus.**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**Concave Polygons**Convex 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.**not a polygon**polygon