A polygon that has all sides the same measure and all angles the same measure is called what?
Answer: A regular polygon.
According to Euclidean Geometry, a polygon that has all angles of the same measure and all sides of the same length is known as a regular polygon.
A regular polygon must have the following properties :
- All its sides should be equal
- All its interior angles should be equal
- All its exterior angles should be equal
Let us apply the three properties of a regular polygon and understand this with the example.
We will check whether the equilateral triangle will fulfill all the above three properties of a regular polygon or not.
We observe that:
The above triangle has all sides equal: AB = BC = CA.
All interior angles measure 60º angles.
All exterior angles measure 120º angles.
Hence, the above triangle ABC is a regular polygon.