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Document related concepts
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Transcript 
triangle
3 sides
triangle
3 sides
quadrilateral
4 sides
triangle
3 sides
quadrilateral
4 sides
pentagon
5 sides
triangle
3 sides
hexagon
6 sides
quadrilateral
4 sides
pentagon
5 sides
triangle
3 sides
quadrilateral
4 sides
hexagon
6 sides
heptagon
(septagon)
7 sides
pentagon
5 sides
triangle
3 sides
quadrilateral
4 sides
hexagon
6 sides
heptagon
(septagon)
7 sides
pentagon
5 sides
octagon
8 sides
nonagon
9 sides
nonagon
9 sides
decagon
10 sides
nonagon
9 sides
decagon
10 sides
11-gon
11 sides
nonagon
9 sides
dodecagon
12 sides
decagon
10 sides
11-gon
11 sides
nonagon
9 sides
dodecagon
12 sides
decagon
10 sides
n-gon
n sides
11-gon
11 sides
nonagon
9 sides
dodecagon
12 sides
decagon
10 sides
11-gon
11 sides
n-gon
n sides
pentadecagon
15 sides
triangle
180º
quadrilateral
2(180º)
360º
pentagon
3(180º)
540º
hexagon
4(180º)
720º
Theorem 55: The sum Si of the measures of
the angles of a polygon with n sides is given
by the formula:
Si = (n – 2)(180)
Three linear pairs.
3(180) = 540
Three linear pairs.
3(180) = 540
The interior angles
have a sum of 180.
Three linear pairs.
3(180) = 540
The interior angles
have a sum of 180.
540 – 180 = 360
Four linear pairs.
4(180) = 720
The interior angles
have a sum of 360.
720 – 360 = 360
Five linear pairs.
5(180) = 900
The interior angles
have a sum of 540.
900 – 540 = 360
Theorem 56: If one exterior angle is taken at
each vertex, the sum Se of the exterior angles
of a polygon is given by the formula:
Se = 360
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
Definition: Diagonal
A diagonal of a polygon is any
segment that connects two
nonconsecutive (nonadjacent)
vertices of the polygon.
triangle:
no diagonals
qudrilateral
2 diagonals
hexagon
9 diagonals
pentagon
5 diagonals
1
2
3
4
4
5
6
7
8
8
9
10
11
11
12
13
13
14
Theorem 57: The number of digonals that
can be drawn in a polygon of n sides is given
by the formula:
Theorem 55: The sum Si of the measures of
the angles of a polygon with n sides is given
by the formula:
Si = (n – 2)(180)
Theorem 55: The sum Si of the measures of
the angles of a polygon with n sides is given
by the formula:
Si = (n – 2)(180)
Theorem 56: If one exterior angle is taken at
each vertex, the sum Se of the exterior angles
of a polygon is given by the formula:
Se = 360
Theorem 55: The sum Si of the measures of
the angles of a polygon with n sides is given
by the formula:
Si = (n – 2)(180)
Theorem 56: If one exterior angle is taken at
each vertex, the sum Se of the exterior angles
of a polygon is given by the formula:
Se = 360
Theorem 57: The number of digonals
that can be drawn in a polygon of n
sides is given by the formula:
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