# Convex, Concave and Self-Intersecting Polygons - Lesson+Exploration+Practice

- Author:
- Simona Riva

## Simple and self-intersecting polygons

In the app below you can see a

*polygon:*polygon is a word derived from Greek, and means "many angles". A polygon can be*simple*, when its boundary does not cross itself, otherwise it's*self-intersecting*. Drag the vertices of the polygon (green points) and create*simple*and*self-intersecting*figures. The intersection points will be shown in orange.## Convex and Concave Polygons

When polygons are

*simple*, we can characterize them further, as*convex*or*concave*. Explore the applet below, create a few different*convex*and*concave*polygons, observe the measure of the angles and the position of the diagonals with respect to the portion of the plane enclosed within its sides. Formulate your own conjecture about how to differentiate a*convex*and a*concave*polygon, depending on these properties of the figure.## Convex polygons and interior angles

What can you say about the measures of the interior angles of a *convex *polygon?
Do they all have a common characteristic?

## Concave polygons and interior angles

What can you say about the measures of the interior angles of a *concave* polygon?
Do some of them have a common characteristic?

## Convex polygons, concave polygons and their diagonals

Describe the *difference *between the *position* of the *diagonals* of a *convex *and of a *concave *polygon, with respect to the portion of the plane enclosed within its sides.