Polygons

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```					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
   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
2
 What is the sum of the angles
 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

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