Vertices Exam Preparation

Introduction :

              In geometry the vertices are the points where the first derivative of curvatures is zero. The two lines are meeting at a vertex they forms the angle. In polygons, angle between the vertices are called as interior angle of the polygon. In solid geometry, a vertex is a point and there are two or more points meet each other. In this article we shall discuss about the topic vertices exam preparation.

 

More about vertices exam preparation:

 

           The vertices are defined as the points of the intersection of the lines or the edges of the polygonal shapes and the geometric shapes. For all the polygonal shape there are vertices. And in the conic sections the vertices are defined as the points at which the shape changes direction.  

Vertices in the conic sections:

           In the conic sections the vertices are the points at which they change their direction. In parabola the point at which the direction of the parabola changes is called as the vertex point. In the hyperbola there are two vertex each for an arm. And the distance between the two vertices of the hyperbola is called as the semi-major axis of the hyperbola.

    Hyperbola vertices

For a parabola the vertex is at a distance a from the center of the parabola.

For the Hyperbola the vertices are at a distance a from the center of the Hyperbola.

Polygon Vertices:

           In the polygons the vertices are the points at which the edges of the shapes meet. And the polygons are named according to the number of vertices in the polygon. And the number of vertices can be used to calculate the internal and the external angle of the regular polygons. And the formulas for calculating the internal angle and the external angle of the  regular polygons using the number of vertices n in the polygon are,

Internal angle = `((n-2)*180)/n` degrees

External angle = `360/n` degrees

Polygon vertices

 

Example problem on vertices exam preparation:

 

1. Calculate the internal angle and the external angle of the regular polygon with 6 vertices.

Solution:

Internal angle = `((n-2)*180)/n` degrees

     = `((6-2)*180)/6`

     = `(4*180)/6`

     = `720/6`

     = `"120 degrees"`

External angle = `360/n` degrees

     = `360/6`

     = `"60 degrees"` 

 

Practice problem on vertices exam preparation:

1. Calculate the internal and the external angle of the polygon with 8 vertices.

    Answer: Internal angle = 135o and External angle = 45o