NAMING

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NAMING POLYGONS
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Let's Discuss
What does the word polygon mean?
What is the smallest number of sides a polygon
can have?
What is the largest number of sides a polygon can
have?
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Triangle
Octagon
Quadrilateral
Nonagon
Pentagon
Decagon
Dodecagon
Hexagon
n-gon
Heptagon
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Hip Bones connected to theClassifying Polygons
Polygons with 3 sides Triangles Polygons with 4
sides Quadrilaterals Polygons with 5 sides..
Pentagons But wait we have more
polygons Polygons with 6 sides
Hexagons Polygons with 7 sides
Heptagons Polygons with 8 sides Octagons But
still we have more polygons Polygons with 9
sides Nonagons Polygons with 10 sides
Decagons Polygons with 12 sides Dodecagons And
now we have our polygons
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Important Terms
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More Important Terms
EQUILATERAL - All sides are congruent
EQUIANGULAR - All angles are congruent
REGULAR - All sides and angles are congruent
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Polygons are named by listing its vertices
consecutively.
A
B
C
F
E
D
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Polygons can be CONCAVE or CONVEX
CONCAVE
CONVEX
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Ex. 3 Classify each polygon as convex or concave.
Concave
Concave
Concave
CONVEX
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Diagonals Angle Measures
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REVIEW
What is the sum of the measures of the interior
angles of a triangle?
180
180
180
What is the sum of the measures of the interior
angles of any quadrilateral?
360
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Sum of measures of interior angles
of triangles
of sides
1(180) 180
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1
2(180) 360
4
2
3
3(180) 540
5
6
4
4(180) 720
n-2
(n-2) ?180
n
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If a convex polygon has n sides, then the sum of
the measure of the interior angles is
(n 2)(180)
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Ex. 1 Use the regular pentagon to answer the
questions.

• Find the sum of the measures of the interior
  angles.
• Find the measure of ONE interior angle

540
108
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Two more important terms
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If any convex polygon, the sum of the measures of
the exterior angles, one at each vertex, is 360.
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If any convex polygon, the sum of the measures of
the exterior angles, one at each vertex, is 360.
1
3
2
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If any convex polygon, the sum of the measures of
the exterior angles, one at each vertex, is 360.
1
2
4
3
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Ex. 2 Find the measure of ONE exterior angle of
a regular hexagon.
60
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Ex. 3 Find the measure of ONE exterior angle of
a regular heptagon.
51.4
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Ex. 4 Each exterior angle of a polygon is 18?.
How many sides does it have?
n 20
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Ex. 5 The sum of the measures of five interior
angles of a hexagon is 535. What is the measure
of the sixth angle?
185
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Ex. 6 The measure of the exterior angle of a
quadrilateral are x, 3x, 5x, and 3x. Find the
measure of each angle.
30, 90, 150, and 90
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Ex. 7 If each interior angle of a regular polygon
is 150?, then how many sides does the polygon
have?
n 12
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Practice Time Practice Worksheet 10-2
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Homework Page 406 16-32 even Page 411 8-18
all
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Foldable for Formulas
Sum of INTERIOR Angles
ONE INTERIOR Angle
Sum EXTERIOR Angles
ONE EXTERIOR Angle