Opposite vertices are two vertices of any polygon with an even number of sides that have the same number of sides between them.
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A vertex is the highest point of something. 'Vertices' is the plural usage of vertex.
a point has one line and two vertices
The locus of the points equidistant from any two points is a straight line. In a square when the points are two opposite vertices this line will pass trough the other two vertices - extending the diagonal between those other two vertices outside the square.
The definition of vertices is the plural vertex. A vertex is point of intersection of two or more lines. A vertex can also be used to describe the angular point of a polygon, polyhedron, or other shape.
A polygon need not have any lines of symmetry. The maximum number of lines of symmetry is attained if the polygon is regular; and this is the number of sides (or vertices) of the polygon. If a regular polygon has an even number of sides, then the lines of symmetry are those joining opposite vertices, and those joining the mid-points of opposite sides. If the polygon has an odd number of sides/vertices, the lines of symmetry are those joining each vertex to the mid-point of the opposite side.