1. Lesson 3-5
Polygons

2. Definitions
Polygon – a closed plane figure with segments as sides. The sides intersect only at endpoints, and no endpoints are collinear.

3. Definitions Diagonal – a segment that connects two
nonconsecutive vertices.
Regular – a regular
polygon is a polygon
with congruent sides
and angles.

4. Definitions

5. Names Sides Name 3 Triangle 9 Nonagon 4 Quadrilateral 10 Decagon 5
Pentagon 11
Hendecagon 6
Hexagon 12
Dodecagon 7
Heptagon
n – Sided
n-gon 8
Octagon
(Ex) 27 sides
27-gon

6. Assignment Memorize Definitions and Polygon Names
Page For problems 5-7, state the name of the polygon and if the polygon is regular or not regular.

7. Polygon Interior Angle-Sum Theorem
The sum of the measures of the interior angles of an n-sided polygon is (n-2)●180°
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the consecutive exterior angles of any polygon is 360°

8. Example What is the measure of each angle of a regular heptagon?
Heptagon  7 sides , so n=7
Sum of the Interior Angles=(n-2)●180°
=(7-2)●180°=900°
Since there are 7 sides, there must be 7 angles.
So each angle would be = 900°/7= 128.6°

9. Assignment
Page For do only the interior angle calculations.