geometry agenda 1. entrance 2. go over practice 3. quiz 4. 3-4 the polygon angle-sum theorems 5....
TRANSCRIPT
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
• 3 sides Triangle• 4 sides Quadrilateral• 5 sides Pentagon• 6 sides Hexagon• 7 sides Heptagon• 8 sides Octagon• 9 sides Nonagon• 10 sides Decagon• 11 sides Undecagon• 12 sides Dodecagon• n sides 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 3-9Polygon 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 3-10Polygon 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 5exterior angles is360.
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