1. Introduction to Polygons
Lesson 15
Introduction to Polygons

2. What is a polygon?
A polygon is a closed plane figure formed by 3 or more segments such that each segment intersects exactly 2 other segments only at their endpoints and no 2 segments with a common endpoint are collinear The segments that form a polygon are called its sides A vertex of a polygon is the intersection of two sides
An equiangular polygon has all congruent angles
An equilateral polygon has all congruent sides
A regular polygon is both equiangular and equilateral
An irregular polygon is not regular
Remember:
Tick marks for ≅ sides
Arcs for ≅ angles

3. Why are these not polygons?
No segments
Not a plane figure
Only 2 segments
Not closed
Intersects more than 2 segments
One side is not a segment

4. Names for polygons (also on page 90)
These are the names of polygons you need to know For a number of sides not listed you use the number of sides with –gon For example a 15 sided polygon can be called a 15-gon However there are names for polygons with more than 12 sides Take time now and research names for polygons over 12 sides

5. Diagonals of a Polygon
Diagonal of a polygon is a segment that connects 2 nonconsecutive vertices 𝐴𝐶 and 𝐷𝐵 are the diagonals of this polygon This polygon is a convex polygon since all diagonals are in the interior of the polygon Convex irregular quadrilateral

6. Diagonals of a Polygon
This polygon is a concave polygon since the diagonal 𝐴𝐷 contains exterior points What is the best name of this polygon? Concave pentagon Concave polygons are always irregular, no need to include when naming

7. Interior and Exterior Angles
Exterior angle of a polygon is formed by extending one of the sides, ∠4 ∠1, ∠2, ∠3 are interior angles Find the measure of all angles m ∠1 = 88° m ∠2 = 57° m ∠3 = 35° m ∠4 = 145°

8. Questions/Review
This lesson was just an introduction to polygons Other lessons will include more about angles, area, perimeter, diagonals, special types of polygons, etc.