Polygon
A polygon is a closed figure made by joining line segments, where each line segment intersects exactly two others.
Examples:
The following are examples of polygons:

The figure below is not a polygon, since it is not a closed figure:

The figure below is not a polygon, since it is not made of line segments:

The figure below is not a polygon, since its sides do not intersect in exactly two places each:

Regular Polygon
A regular polygon is a polygon whose sides are all the same length, and whose angles are all the same. The sum of the angles of a polygon with n sides, where n is 3 or more, is 180° × (n - 2) degrees.
Examples:
The following are examples of regular polygons:

Examples:
The following are not examples of regular polygons:

Vertex
1) The vertex of an angle is the point where the two rays that form the angle intersect.

2) The vertices of a polygon are the points where its sides intersect.

Triangle
A three-sided polygon. The sum of the angles of a triangle is 180 degrees.
Examples:

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