Polygons Part 1
Polygons
As we begin the lesson on polygons, we must first understand the vocabulary used with two-dimensional figures.
We will then study in depth the polygon with the least number of sides possible in order to understand the properties of polygons with more sides.
Vocabulary
- polygon
- vertex
- side
- diagonal
- convex
- concave
- n-gon
- equilateral polygon
- equiangular polygon
A polygon is a closed figure with a finite number of sides which are line segments.
An angle formed by the intersection of two sides is called a vertex of the polygon.
A polygon has to meet the following three criteria:
- a polygon must have at least three sides
- all sides must be line segments
- each side intersects exactly two other sides, one at each endpoint
Not Polygons
Parts of a Polygon
Here is an example of a polygon. Remember each endpoint is called a vertex. Plural for vertex is vertices. We would say this polygon had four vertices.
You name a polygon by listing the vertices consecutively. It does not matter which endpoint you start with or if you go clockwise or counterclockwise rotation. We could name the polygon above as polygon ABCD or ADCB and still be correct.
Convex Polygons
Diagonals are helpful in determining if a polygon is convex or concave.
A polygon is considered convex if none of the diagonals of the polygon are outside of the figure.
Concave Polygons
A polygon is classified as concave if at least one diagonal is outside of the polygon. Notice how diagonal AB is outside of the polygon, thus concave.
Convex or Concave
OPTIONAL way to determine if a polygons are convex or concave:
To check, extend the lines containing each side. If any of the lines contain any point in the interior of the polygon, then it is concave. Otherwise it is convex.
Concave: See the purple areas inside the polygon?
Your Turn
Identify if the polygons are convex or concave.
Answer: Concave
Answer: Convex
Answer: Convex
Answer: Convex
Answer: Concave
Answer: Concave
