Line Segment

How Do You Construct A Line Segment

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Construction Of A Line Segment

To draw a line segment of a given length

We can draw a line segment of a given length in two ways:
(a) By using a scale
(b) By using a pair of compasses

Construction: Draw a line segment of length 5.5 cm.

(a) By using a scale

  • Step 1: Mark a point in your notebook and label it as A.
    Construction-of-Line-Segment
  • Step 2: Place the scale in such a way that the zero (0) mark on the scale coincides with A.
    Construction-of-Line-Segment-1
  • Step 3: How, move the sharp end of the pencil along the edge of the scale till it reaches the point 5.5 cm of the scale,
    Construction-of-Line-Segment-2
  • Step 4: Label the second end as B.
    AB is the required line segment.
    Construction-of-Line-Segment-3

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(b) By using a pair of compasses

  • Steps 1: Draw a line l and mark a point A on it.
    Construction-of-Line-Segment-4
  • Step 2: Open the arms of the compass so that the end points of the two open arms equal to 5.5 cm.
    Construction-of-Line-Segment-5
  • Step 3: Without disturbing the opening of the compasses, place its needle at point A and draw an arc to cut the line l at point B.
    Construction-of-Line-Segment-6
  • Step 4: AB is the required line segment of length 5.5 cm.
    Construction-of-Line-Segment-7

To draw a line segment equal to a given line segment

Construction: Draw a line segment (AB) equal to PQ.
Given: A line segment PQ.
Construction-of-Line-Segment-8

  • Step 1: Draw a line l. Mark a point A on it.
    Construction-of-Line-Segment-9
  • Step 2: Take the compass and measure PQ.
    Construction-of-Line-Segment-10
  • Step 3: Without disturbing the opening, place the needle of the compass at point A on line l and draw an arc, which cuts the line at point B.
    Construction-of-Line-Segment-11
  • Step 4: AB is the required line segment which is equal to the length of PQ, i.e., AB = PQ.
    Construction-of-Line-Segment-12

Construction: Draw a line segment whose length is the sum of the lengths of two given line segments.
Given: Two line segments AB and BC.
Construct a line segment, say AC, such that
AC = AB + BC.
Construction-of-Line-Segment-13

  • Step 1: Draw a line l and mark point A on it.
    Construction-of-Line-Segment-14
  • Step 2: Take the compasses and measure AB.
    Construction-of-Line-Segment-15
  • Step 3: Without disturbing the opening, place its needle at A and draw an arc cutting line l at B.
    Construction-of-Line-Segment-16
  • Step 4: Again adjust the compasses and measure the line segment BC.
    Construction-of-Line-Segment-17
  • Step 5: Without disturbing the opening, place the pointer at point B on the line l and draw an arc cutting the line l at C.
    Construction-of-Line-Segment-18
  • Step 6: AC is the required line segment whose length is equal to the sum of the lengths of line segments AB and BC, i. e., AC = AB + BC.

What are the Basic Elements in Geometry

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The Basic Elements of Geometry

You are familiar with some terms like triangle, square, cube, cuboid, etc. These are examples of geometrical figures. To make these geometrical figures we need to know some basic elements. These basic elements are as follows:

Point(.): A point gives an idea of a location, by making a dot by a sharp pencil on a paper. It has no length, breadth, or thickness. It has just a position and only its location can be determined.
A point is denoted by a capital letter of the alphabet like A, B, C, etc.
For example:   . P (This is point P.)

Line (↔): A line is a collection of points, which can be extended endlessly on both the sides. It has length only. It has neither breadth nor thickness.
A line can be denoted in two ways
(i) Denote it by a small letter of the alphabet like line l as shown in Fig.
Line (ii) Mark two points (say A and B) on the line as shown in Fig. and denote it by \(\overleftrightarrow{\text{AB}}\) or line AB.
Line-1

Line Segment ( ¯ ): A Line segment is a part of a line that is bounded by two distinct end points. It has a definite length but no breadth and thickness. It is the shortest distance of any two points.
A line segment from A to B is represented by seg AB or \(\overline{\text{AB}}\) or \(\overline{\text{BA}}\).
Line-segmentThis is seg AB or \(\overline{\text{AB}}\).

Ray (→): A ray is also a part of a line which has only one end point and can be extended endlessly in one direction. A ray has no breadth or thickness.
A ray is represented by \(\overrightarrow{AB}\). It shows that A is the fixed point and B is a point on the path of a ray.
RayLight coming from the sun or torch is an example of a ray.

Comparison between line, line segment, and ray
Table shows the comparison between line, line segment, and ray.

Line

Line Segment

Ray

1. A line has no definite length,A line segment has definite length.A ray has no length.
2. A line has no end points.A line segment has two end points.A ray has one end point.
3. A line has no thickness.A line segment has no thickness.A ray has no thickness.
4. A line AB is represented by \(\overleftrightarrow{\text{AB}}\)A line segment AB is represented by \(\overline{\text{AB}}\).A ray AB is represented by \(\overrightarrow{AB}\).

Plane: A plane is a flat smooth surface that extends indefinitely in all directions. It has length and breadth but no thickness.
The top of a table, top and bottom of a cylinder, surface of a blackboard, etc. give the idea of a plane.
planeA plane can be denoted by taking three or more points on it, which do not lie on the same line. Plane-1

Incidence properties in a plane
The relationship between a point and a line in a plane is called the incidence property. It states that
Plane-2

  1. Infinite number of lines can be drawn passing through a given fixed point in a plane.
    Lines l1, l2, l3, l4, …… all pass through a point A.
  2. One and only one line can be drawn passing through two given points in a plane.

If A and B are the two points in a plane, then l2 becomes the unique line that passes through the points A and B.
Plane-3

COLLINEAR POINTS
Three or more points are said to be collinear, if they lie on the same line in a plane. This line is called the line of collinearity.
collinear-pointsIn the above Fig. points A, B, and C lie on the same straight line l, so they are collinear points. If a straight line in a plane contains two points but it does not contain the third point, then these three points are said to be non-collinear. In the below Fig. A, B, C are non-collinear.
collinear-points-1