POLYGONS II-TEACHER HATIFA-What is a Polygon????

Any ideas?Write down what you think it is for #1.A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).

Classifying Polygons by # of Sides3 sided Polygon = Triangle

Hint: Think Tricycle, tripod, Trilateration (Tri means 3)

Classifying Polygons by # of Sides4 sided Polygon = QuadrilateralHint: Think Quadrant, Quadruple, Quad (AKA 4-Wheeler)

Classifying Polygons by # of Sides5 sided Polygon = PentagonHint: Think Pentathalon, or the government building The Pentagon

Classifying Polygons by # of Sides6 sided Polygon = HexagonHint: Both Hexagon and Six have an x in them

Classifying Polygons by # of Sides7 sided Polygon = HeptagonHint: ???

Classifying Polygons by # of Sides8 sided Polygon = OctagonHint: octopus 8 legs

Classifying Polygons by # of Sides9 sided Polygon = NonagonHint: Non is similar to Nine

Classifying Polygons by # of Sides10 sided Polygon = DecagonHint: Think Decade (10 years

Classifying Polygons by # of Sides# of SidesName3Triangle4Quadrilateral5Pentagon6Hexagon7Heptagon8Octagon9Nonagon10Decagon11Hendecagon12DodecagonTwo Types of PolygonsConvex all vertices point outwardConcave at least one vertex points inward towards the center of the polygon (The side looks like it caved in)

Regular PolygonsA Regular Polygon is a polygon in which all sides are the same length.

Equilateral Triangle SquareReview of Similar Triangles

2 Triangles are similar if they have the same shape (i.e. the same angle in the same positions)Similar PolygonsThe same is true of polygons. 2 polygons are similar if they have the same angles in the same positions (i.e. same shape)

^ Similar Pentagons ^Similar Trapezoids Similar Rectangles EQ: How do I find the measure of an interior & exterior angle of a polygon?FABCDEA VERTEX is the point of intersection of two sidesA segment whose endpoints are two nonconsecutive vertices is called a DIAGONAL.CONSECUTIVE VERTICES are two endpoints of any side. Sides that share a vertex are called CONSECUTIVE SIDES. IMPORTANT TERMS Let us find the connection between the number of sides, number of diagonals and the number of triangles of a polygon.Polygons QuadrilateralPentagon180o180o180o180o180o2 x 180o = 360o 3 4 sides5 sides3 x 180o = 540oHexagon6 sides180o180o180o180o4 x 180o = 720o 4 Heptagon/Septagon7 sides180o180o180o180o180o5 x 180o = 900o 5 2 1 diagonal2 diagonals 3 diagonals 4 diagonals Polygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Polygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Quadrilateral4122 x1800= 36003600/4= 900Polygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Quadrilateral4122 x1800= 36003600/4= 900Pentagon5233 x1800= 54005400/5= 1080Polygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Quadrilateral4122 x1800= 36003600/4= 900Pentagon5233 x1800= 54005400/5= 1080Hexagon6344 x1800= 72007200/6= 1200Polygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Quadrilateral4122 x1800= 36003600/4= 900Pentagon5233 x1800= 54005400/5= 1080Hexagon6344 x1800= 72007200/6= 1200Heptagon7455 x1800= 90009000/7= 128.30Polygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Quadrilateral4122 x1800= 36003600/4= 900Pentagon5233 x1800= 54005400/5= 1080Hexagon6344 x1800= 72007200/6= 1200Heptagon7455 x1800= 90009000/7= 128.30n sided polygonnAssociation with no. of sides Association with no. of sidesAssociation with no. of trianglesAssociation with sum of interior anglesPolygons RegularPolygonNo. of sidesNo. of diagonalsNo. ofSum of the interior anglesEach interior angleTriangle30118001800/3= 600Quadrilateral4122 x1800= 36003600/4= 900Pentagon5233 x1800= 54005400/5= 1080Hexagon6344 x1800= 72007200/6= 1200Heptagon7455 x1800= 90009000/7= 128.30n sided polygonnn - 3n - 2(n - 2) x1800(n - 2) x1800 / nPolygons

Septagon/HeptagonDecagonHendecagon7 sides10 sides11 sides9 sidesNonagonSum of Int. Angles 900oInterior Angle 128.6oSum 1260oI.A. 140oSum 1440o I.A. 144oSum 1620o I.A. 147.3oCalculate the Sum of Interior Angles and each interior angle of each of these regular polygons.1243Polygons 2 x 180o = 360o360 245 = 115o3 x 180o = 540o540 395 = 145oy117o121o100o125o140oz133o137o138o138o125o105oFind the unknown angles below.Diagrams not drawn accurately.

75o100o70owx115o110o75o95o4 x 180o = 720o720 603 = 117o5 x 180o = 900o900 776 = 124oPolygons Polygons An exterior angle of a regular polygon is formed by extending one side of the polygon.Angle CDY is an exterior angle to angle CDE Exterior Angle + Interior Angle of a regular polygon =1800DEYBCAF12Polygons 120012001200600600600Polygons 120012001200Polygons 120012001200Polygons 3600Polygons 600600600600600600Polygons 600600600600600600Polygons 123456600600600600600600Polygons 123456600600600600600600Polygons 1234563600Polygons 900900900900Polygons 900900900900Polygons 900900900900Polygons 12343600Polygons No matter what type of polygon we have, the sum of the exterior angles is ALWAYS equal to 360. Sum of exterior angles = 360Polygons In a regular polygon with n sides

Sum of interior angles = (n -2) x 1800Exterior Angle + Interior Angle =1800

Each exterior angle = 3600/n

No. of sides = 3600/exterior angle

Polygons