what is a concave polygon using the classify and differentiate method
To understand what a concave polygon is, let's use the classify and differentiate method.
Step 1: Understand polygons
A polygon is a closed shape consisting of straight sides. Each side is called an edge, and each point where two sides meet is called a vertex. Examples of polygons include triangles, squares, and pentagons.
Step 2: Classify polygons based on angles
To differentiate between different types of polygons, we can classify them based on their angles. There are two broad categories: concave and convex polygons.
Step 3: Concave polygons
A concave polygon is a polygon with at least one interior angle greater than 180 degrees. In simpler terms, if you draw a line segment between two points inside a concave polygon, that line segment will intersect the boundary of the polygon at least twice.
Step 4: Differentiating concave and convex polygons
To differentiate between concave and convex polygons, you can use the following method:
1. Draw a line segment between two points inside the polygon.
2. Check if the line segment intersects the boundary of the polygon more than twice.
3. If it does, the polygon is concave. If it doesn't, the polygon is convex.
Step 5: Examples
Let's take some examples to understand this better:
Example 1: Triangle
A triangle has three sides and three angles. All angles of a triangle are less than 180 degrees, so it does not have any angle greater than 180 degrees. Therefore, a triangle is always a convex polygon.
Example 2: Regular hexagon
A regular hexagon has six sides and six angles. All the angles of a regular hexagon are equal to 120 degrees (360 degrees divided by 6). None of these angles is greater than 180 degrees, so a regular hexagon is also a convex polygon.
Example 3: Concave polygon
Consider a shape with five sides where one of the interior angles is 220 degrees. If we draw a line segment between two points inside this shape, it will intersect the boundary of the shape more than twice. Thus, this shape is a concave polygon.
In summary, a concave polygon is a polygon with at least one interior angle greater than 180 degrees, where a line segment drawn between two points inside the polygon intersects the boundary more than twice.