Polygons

							Polygons


Where has Polly gone?
Polygon

  A closed figure formed by joining three or
   more segments in a plane at their
   endpoints, with each line segment joining
   exactly 2 others.
  Each line segment is called a side of the
   polygon.                   This polygon
                             has 8 sides.
Circle the figures that are
polygons:
Why are these NOT
polygons?
  A. Open side

  B. Curved side
  C. Vertex has
   more than 2
   segments that
   meet
  D. Curved side
Vertex and diagonal

  A vertex is where 2 sides meet.
  A diagonal joins two
   nonconsecutive vertices.
  Name the vertices and the
   diagonal in this polygon:
  Vertices: A,B,C,D,E,F
  Diagonal: CE
List all the diagonals in
this polygon:
    DB
    DA
    EC
    EB
    AC
Polygons are named by
the number of sides.
    Name these polygons:

   A. triangle
   B. Quadrilateral
   C. Pentagon
   D. Hexagon
   E. Octagon
   F. Dodecagon
Polygons with all sides and angles
equal are regular polygons. Circle
the regular polygons:
Polygons are named by
naming consecutive vertices
in order.
  Circle all the correct
   names for this polygon:
 pentagon ABCDE
 pentagon AEDCB
 pentagon ACDBE
 pentagon DCBAE
 pentagon BDCAE
 pentagon BAEDC
What is the sum of the angle
measures in a triangle?
  Please draw a triangle on a piece of
   scratch paper. It can be any size or
   shape, just be sure it is a triangle.
      Now, tear off the three angles of the
       triangle. Position the angles side-by-side
       on your desk. What shape do they
       make?




Draw the angles side-by-side on your paper like this ↑
What is the measure of a
straight line?
  The sum of the angles of
  any triangle is 180°
 Find the measure of
  the missing angle:    35°
 ‫)53+ 09( - 081 = 1ے‬
 ‫)521( - 081 = 1ے‬      90°   ‫1ے‬
 ‫°55 = 1ے‬
  The sum of the angles of
  any triangle is 180°
 Find the measure of
  the missing angle:
                               ‫2ے‬
 ‫)56 + 56( - 081 = 2ے‬
 ‫)031( - 081 = 2ے‬
 ‫°05 = 2ے‬
                         65°        65°
Find x:


  3x - 4 + 5x + 10 + 6x + 6 = 180
  14x + 12 = 180
       -12 -12
  14x = 168
     x = 12
 What is the sum of the angle
 measures in a polygon?
 We can divide the polygon
  into triangles, then multiply
  the number of triangles by
  180°
 How many triangles make up
  this quadrilateral?
2
 What is the sum of the angles
  of this quadrilateral?
 2 x 180° = 360°
What is the sum of the
angles in this hexagon?
  4 x 180° =
    720°
What is the sum of the
angles in this pentagon?
  3 x 180° =
    540°
 Do you HAVE to draw the triangles
 to find out how many of them there
 are in a polygon?
    NO!




4 sides,        5 sides,         6 sides,
2 triangles   3 triangles      4 triangles

                n sides,
              n-2 triangles!
What is the sum of the
measures of the angles of
these polygons?




180(6-2)   180(8-2)   180(10-2)
= 180(4)   =180(6)    = 180(8)
= 720°     = 1080°    =1440°
 Find the missing angle
 measure in this polygon:

 180(5-2)
 = 180(3)
 = 540°

 540° = 115 + 106 + 94 + 109 + X
 540 = 424 + X
 116° = X
Find the missing angle
measure in this polygon:
  180(9-2)
  = 180(7)
  = 1260°

  1260° = 156 + 151 +
   138 + 156 + 140 +
   130 + 133 + 135 +X
  1260 = 1139 + X
  121° = X