Introduction
A point and a line are considered as one of the most fundamental building blocks of geometry.A line segment, a ray and a plane are the geometrical objects which can not be drawn without the help ofa point and line.
This chapter discusses the definitions and examples of point, line, ray, line segment and a plane.How two or more than two lines can make when meet at some point for example intersecting lines, perpendicularlines, parallel lines, transversal lines and concurrent lines with the helpof diagrams. FAQs, Solved Examples and MCQs related to points, lines, rays, line segments and planes have beengiven at the end of the chapter to go through the example questions and to practice more questions.
What is a Point in Geometry?
In geometry, when we mark the exact position of an object with a dot, that is called a point. It has no lengthand breadth. Also, it occupies no depth. In other words, a point determines a location.
It is denoted by a dot “∙” symbol.
We use capital letters of alphabets to name a point.
Example
∙ A (read as point A)
∙ X (read as point X)
Two points A and X
What is a Line in Geometry?
A Line is a one dimensional figure which is straight, has indefinite length and no thickness. Line can be extendedindefinitely only in two directions which are opposite to each other.A line has an infinite number of points lying on it.
A line has no end points.
We can name the lines by using two capital letters of alphabets and an arrow that points in both directions.
Example
Line AB
What is a Ray in Geometry?
It is a straight line which starts from one fixed point and always progress in one direction only away from thatstarting point. Ray can be extended indefinitely only in one direction.
It has one end point. It has no definite length and can’t be measured.
Ray is represented by two capital letters of alphabets with a pointed arrow on top of it.
Example
where, A is the starting fixed point of the ray.
Ray AB
What is a Line Segment in Geometry?
A Line segment is a part or segment of a line that is bounded by two distinct end points those lie on that line.A Line segment has a number of other points lying on it, but they all lie in between the two end points only.
Line segment is also represented by two capital letters of alphabets but with a line on top of it.
Example
Line segment AB
What is a Plane in geometry?
In geometry, a plane is a flat and smooth surface. It has length and width. It has no thickness. Plane can beextended indefinitely in all directions.
Example of a Plane
We can name the plane by using English alphabets. For example, the plane drawn in the above diagram can be namedwith letters A, B and C and called as Plane ABC.
Another example of a Plane
This plane can be named with letters P, Q, R and S and called as Plane PQRS.
The real life examples of a plane, that can we see around us and everywhere are surface of a wall and ceiling ofa room.
What are Intersecting lines?
Lines are said to be intersecting lines if they meet out at a point.
Intersecting lines AB and CD
Line AB and line CD intersect each other at a point E.
What are Perpendicular lines?
The lines are said to be perpendicular lines if they intersect each other and the angle between them is90°.
Perpendicular lines AB and CD
Lines AB and CD intersect at O and form an angle of 90° in each quadrant.
Line AB is perpendicular to line CD. To denote AB is perpendicular to CD, we usesymbol ⊥.
So, we can write it as AB ⊥ CD or we can write as CD ⊥ AB.
What are Parallel lines?
Two straight lines are said to be parallel lines if they do not intersect each other at any point although weextend these line in both directions indefinitely.
Parallel lines AB and CD
Line AB is parallel to CD. To denote it, we can use symbol ||. So. it is written as AB||CD orCD||AB.
What is a Transversal line?
A line is said to be a transversal line, if it cuts two or more lines at different points and those lines can beparallel or non parallel lines.
Transversal lines AB and CD
Here, line AB cuts through two lines PQ and RS where line AB is called as transversal line.
What are Concurrent lines?
If three or more straight lines pass through the same point or intersect each other at same point, then theselines are called concurrent lines.
The point where lines intersect each other, is called point of concurrence.
Concurrent lines AB, CD, PQ and RS
Here, AB, CD, PQ and RS are concurrent lines, as these lines pass through the same point T. T is called thepoint of concurrence.
