Transcript Geometry

Geometry
• Agenda
1. ENTRANCE
2. Go over Practice
3. Quiz
4. 3-4 The Polygon Angle-Sum Theorems
5. Practice Assignment
6. EXIT
Practice
• Quiz Time
Good Luck!!!
Chapter 3
3-4 The Polygon Angle-Sum
Theorems
Polygon
• A _______ figure that consists of three or
more segments joined at the endpoints
and each segment must meet exactly two
other segments.
Polygon Terms
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3 sides
4 sides
5 sides
6 sides
7 sides
8 sides
9 sides
10 sides
11 sides
12 sides
n sides
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Undecagon
Dodecagon
n-gon
Naming A Polygon
• A polygon is named by the number of
_______.
ex: If a polygon has
___ sides, you use
___ letters.
Polygon ABCDE
Types of Polygons
• Convex
– The diagonals are entirely inside the figure.
• Concave
– At least one diagonal is partly outside the
figure.
Regular Polygon
• Remember: equilateral, equiangular
• A regular polygon is a polygon that is both
equilateral and equiangular.
Theorem 3-9
Polygon Angle-Sum Theorem
• The sum of the measures of the angles of
an n-gon is (n-2)180.
ex: This pentagon
has 5 sides.
Sum = (n-2)180
Sum = (5-2)180
Sum = (3)180
Sum = 540
Theorem 3-10
Polygon Exterior Angle-Sum
Theorem
• The sum of the measures of the ________
angles of a polygon, one at each vertex, is 360.
ex: This pentagon
has 5 sides.
The sum of the 5
exterior angles is
360.
Example #1
• Name the ________. Identify vertices,
sides, and angles. Is it concave or
convex?
Example #2
• Find the interior angle sum.
a. 13-gon
b. decagon
Example #3
• How many sides does each polygon have
if its interior angle sum is:
a. 2700
b. 1080
Example #4
• Find x.
Example #5
• Find y.
Example #6
• Find x.
Example #7
• Find x.
Example #8
• Find x.
Example #9
• How many sides does each regular
polygon have if its exterior angle is:
a. 120
b. 24
Example #10
• How many sides does each regular
polygon have if its interior angle is:
a. 90
b. 144
• Practice
– WB 3-4 # 1-19
• EXIT