What is the Difference Between an Internal and an External Division of a Line Segment?

What is Line Segment- Line segment is a part of a line which has two distinct end points and will always have each and every point on the line that is middle of the endpoints. If we consider a line segment which is closed then that will have both the endpoints. An open line segment thus will not have any endpoint and a half open line segment will have only one endpoint. In the field of Geometry we can say that a line above the endpoints will be considered as a line segment.

Examples- Sides of a Square. This is a typical example of Line segment. When we consider both the endpoints which are nothing but the vertices, then we are here saying about a polygon or polyhedron. Here the line segment is n the edge if they lie on the adjacent sides or they are either diagonal ones. If we are considering a curve then the end points will be one the line and here the line segment is thus called a CURVE.

Properties for Line Segments: 

  1. Every line segment is always connected and this is never empty.
  2. IF we consider a vector space then a corresponding line segment will be a closed set inside the vector set. A open line segment is an open set always and this is always one dimensional.
  3. We can define line segment in ordered geometry as a pair of line segments which is defined by the following concepts or functions – intersection, parallel etc. We can also say that Line segment are aways different from lines. IF we have two nonparallel lines in the same plane then they are bound to always cross over each other and also they do not thus satisfy the law of segments.
  4. In some geometry structures we can assume the condition of such line segments in certain ways like axioms, or even isometry of a line. This is thus used in the coordinate system.
  5. Line Segments always are important for geometrical representation for some theories. IF we take a convex set where the line segments are joint by two points on the set which is inside the set. This is very crucial to note because here we know that it will change the analysis of the convex structure and we will start the analysis of line segment. We can also use the operation of addition to the theories and thus it can help with equal length and also for making statement on system which are congruent.

Line Segment as a degenerate for Ellipse. We can always consider line segments are degenerate ones where the axis which is minor is always zero and the foci will go to the end points and also we can describe this as the set of points where if we calculate the sum of the points distances to the two foci it will always give a constant number.

How do we calculate the LINE SEGMENT in other geometrical shapes- Here we take a intersection which is the point or a line or a curve and both these are very much common to the objects taken into consideration. Here we are talking about Lines or planes or curves. The most common and simple one is the intersection of two lines which appear very distinct.

how to determine line segment in FLATS- Here it is a linear geometrical object and it is embedded in a high dimensional space and thus we apply linear algebra here. However now here we determine intersection which goes well for non linear equations and also we can solve it. Suppose we take a parabola then we can use simple equations to solve it. Intersections between the quadrics will be solved very easily in the field of Algebra.

In case of Triangles- IF we consider segments in a Triangle then we need to check the three altitudes and three medians. also the perpendicular bisector of the sides of the triangle and also the internal angle formed by the bisectors. These are various methods here to be used and also there are various types of inequalities and equal here. Other areas of interest will be where we connect the various triangle centres and notably the orthocenter, the circumcenter and centroid also directed line segments are those where the line segment is given a direction and it will cause a translation or change in the direction. Here the magnitude also changes. Thus the change of the magnitude and direction show the potential change in it. IF we are to extend a directed line will produce a ray and it will also cause infinite amount of line segments along a direction.

Learn more from the concepts of Co-ordinate Geometry from Class 11 Maths