Contents
Polygons:
A polygon is a closed curve (figure) formed by the line segment such that:
1) No two line segments intersect except at their end-points.
2) No two line segments with a common end points are coincident.
The line segments forming a polygon are called its sides and the end-points of the line segments are called its vertices. In other words, the meeting point of a pair of sides is called a vertex of the polygon.
ABC is a polygon having three sides AB, BC and CA. Points A, B, C are known as the vertices. As the figure consists of three sides. So, it is called a triangle.
is a polygon with four sides AB, BC, CD and DA. It has four vertices A, B, C and D. Such a figure is called a quadrilateral. Line segments AC and BD are known as diagonals.
A closed figure formed by five line segments is known as a pentagon.
is a pentagon with AB, BC, CD, DE and EA as five sides. A, B, C, D and E are five vertices of the pentagon. Line segments AC, AD, BD and BE are diagonals.
is not a polygon as BC is not a line segment.
Adjacent Sides:
Any two sides with a common end-point (vertex) are called the adjacent sides of the polygon.
Adjacent Vertices:
The endpoints of the same side of a polygon are known as the adjacent vertices.
Diagonals:
The line segments obtained by joining vertices which are not adjacent are called the diagonals of the polygon.
Convex Polygon:
A polygon is a convex polygon if the line segment joining any two points inside it lies completely inside the polygon.
the line segment joining P and Q does not line completely inside the polygon ABCDE. So, it is not a convex polygon.
Similarly, 
is not a convex polygon.
are convex polygons.