In this page, we practice identifying whether polygons are regular or irregular, convex or concave, and simple or complex.
Example 1
Classify the equilateral triangle.
Solution
Since all three sides and all three angles are equal, the triangle is a regular polygon.
Since all interior angles are less than \(180^\circ\), it is a convex polygon.
Since the sides do not cross each other, it is a simple polygon.
Therefore, the equilateral triangle is a regular, convex, simple polygon.
Example 2
Classify the rectangle.
Solution
The sides are not all equal, so the rectangle is an irregular polygon.
All interior angles are less than \(180^\circ\), so it is a convex polygon.
The sides do not intersect, so it is a simple polygon.
Therefore, the rectangle is an irregular, convex, simple polygon.
Example 3
Classify the concave pentagon shown below.
Solution
Since one interior angle is greater than \(180^\circ\), it is a concave polygon.
Its sides do not cross each other, so it is a simple polygon.
The sides and angles are not all equal, so it is an irregular polygon.
Therefore, the pentagon is an irregular, concave, simple polygon.
Example 4
Classify the five-pointed star whose sides intersect.
Solution
Since the sides cross each other, it is a complex polygon (self-intersecting polygon).
The sides and angles are not all equal, so it is an irregular polygon.
Therefore, the star shape is an irregular, complex polygon.
Practice
- Take the Quiz