Polygons The word ‘polygon’ is a Greek word. Poly

Transcript:Polygons The word ‘polygon’ is a Greek word. Poly:
Polygons The word ‘polygon’ is a Greek word. Poly means many and gon means angles. Polygons Polygons The word polygon means “many angles” A two dimensional object A closed figure More about Polygons Made up of three or more straight line segments There are exactly two sides that meet at a vertex The sides do not cross each other Polygons Examples of Polygons Polygons These are not Polygons Polygons Terminology Side: One of the line segments that make up a polygon. Vertex: Point where two sides meet. Polygons Vertex Side Polygons Interior angle: An angle formed by two adjacent sides inside the polygon. Exterior angle: An angle formed by two adjacent sides outside the polygon. Polygons Interior angle Polygons Let us recapitulate Polygons Types of Polygons Equiangular Polygon: a polygon in which all of the angles are equal Equilateral Polygon: a polygon in which all of the sides are the same length Polygons Regular Polygon: a polygon where all the angles are equal and all of the sides are the same length. They are both equilateral and equiangular Polygons Examples of Regular Polygons Polygons A convex polygon: A polygon whose each of the interior angle measures less than 180°. If one or more than one angle in a polygon measures more than 180° then it is known as concave polygon. (Think: concave has a "cave" in it) Polygons IN TERIOR ANGLES OF A POLYGON Polygons Let us find the connection between the number of sides, number of diagonals and the number of triangles of a polygon. Polygons Quadrilateral Pentagon 180o 180o 180o 180o 180o 2 x 180o = 360o 3 4 sides 5 sides Hexagon 6 sides 4 x 180o = 720o 4 Heptagon/Septagon 7 sides 180o 180o 180o 180o 5 x 180o = 900o 2 diagonals 3 diagonals 4 diagonals Polygons Polygons Polygons Polygons Polygons Polygons Polygons Polygons Septagon/Heptagon Decagon Hendecagon 7 sides 10 sides 11 sides 9 sides Nonagon Sum of Int. Angles 900o Interior Angle 128.6o Sum 1260o I.A. 140o Sum 1440o I.A. 144o Sum 1620o I.A. 147.3o Calculate the Sum of Interior Angles and each interior angle of each of these regular polygons. 1 2 4 3 Polygons 2 x 180o = 360o 360 – 245 = 115o 3 x 180o = 540o 540 – 395 = 145o Find the unknown angles below. Diagrams not drawn accurately. 4 x 180o = 720o 720 – 603 =