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 of a 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, perpendicular lines, parallel lines, transversal lines and concurrent lines with the help of diagrams. FAQs, Solved Examples and MCQs related to points, lines, rays, line segments and planes have been given 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 length
and 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.
∙ A (read as point A)
∙ X (read as point X)
Line in Geometry
A Line is a one dimensional figure which is straight, has indefinite length and no thickness. Line can be extended
indefinitely 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.
is a line.
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 that
starting 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.
is a ray and A is its the fixed starting point.
What is a line segment?
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.
is the line segment.
Plane in geometry
In geometry, a plane is a flat and smooth surface. It has length and width. It has no thickness. Plane can be
extended indefinitely in all directions.
The real life examples of a plane, that can we see around us and everywhere are surface of a wall and ceiling of
a room.
We can name the plane by using English alphabets.
Example 1:
The plane drawn in the diagram is named
with letters A, B and C and called as plane ABC.
Example 2:
This plane can be named plane PQRS with letters P, Q, R and S.
What are Intersecting lines?
Two lines are said to be intersecting lines if they meet out at a point.
In the figure AB and CD are the Intersecting lines. AB and 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 is 90°.
Here, AB and CD are perpendicular 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 use
symbol ⊥.
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 we extend these line in both directions indefinitely.
Line AB is parallel to CD. To denote it, we can use symbol ||. So. it is written as AB||CD or CD || 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 be parallel or non parallel lines.
AB cuts through two lines PQ and RS, the line AB is called 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 these
lines are called concurrent lines.
The point where lines intersect each other, is called point of concurrence.
Here, AB, CD, PQ and RS are concurrent lines, as these lines pass through the same point T. T is called the point of concurrence.
What are collinear points?
If three or more points lie on the same straight line then points are called collinear points.
Here, A, B, C and D are collinear points as they lie in the same straight line.
Frequently Asked Questions
1) What is a point?
A point is a mark of a position.
2) What is a line?
A line refers to a straight line which can be extended indefinitely in both directions.
3) What is a plane?
Plane is a flat surface which can be extended indefinitely in all directions.
Solved Examples
1) Identify ray and line segment from the following figure.
Solution
Ray is
Line segment is
2) Draw a line m and name a line segment AB on line m.
Solution
Here, m is a line and AB is a line segment on it.
3) Check whether following pairs of lines are parallel, intersecting, concurrent or perpendicular?
Solution
- Parallel lines
- Concurrent lines
- Intersecting lines
- Perpendicular lines
4) How many line segments are there in the following figure?
Solution
PQ, PR, PS, QR, QS and RS are six line segments.
Fill in Blanks Worksheet
| Type: | Blanks |
| Count: | 1 |
- The line segment has ___________ length.
- A ray has only ___________ fixed point.
- A line contains ___________ points in it.
- Intersecting lines must meet at a ___________ point.
- The distance between the set of parallel lines remains ___________ .
- In geometry, a ___________ is a flat and smooth surface.
- Perpendicular lines intersect each other at ___________.
- A point has no length, breadth and ___________.
- Rail tracks are an example of ___________ lines.
- If three or more points lie on the same straight line, then the points are called ___________ points.
Write True or False Worksheet
| Type: | True False |
| Count: | 1 |
| S.N. | Statement | ✓ or ✕ |
|---|---|---|
| 1) | Only two lines can be drawn through two given points. | |
| 2) | The intersection of two planes is a straight line. | |
| 3) | A ray has a definite length. | |
| 4) | The infinite number of lines can pass through three collinear points. | |
| 5) | Two parallel lines always lie in the same plane. | |
| 6) | Rays and ray have the same initial point. | |
| 7) | A line has an indefinite length. | |
| 8) | Concurrent lines always meet at the same point. | |
| 9) | A line segment has an indefinite length. | |
| 10) | Intersecting lines meet at two points. |
Geometry Worksheet
| Type: | Geometry |
| Count: | 1 |
- Name any two lines.
- Name any two line segment.
- Name any two pairs of parallel lines.
- Name any two pairs of intersecting lines.
- Name any two transversal lines.
- Name the collinear points.
- Name the point of intersection of any two intersecting lines.
- Name the concurrent lines with point of concurrence.
Multiple Choice Questions Worksheet
| Type: | MCQ |
| Count: | 1 |
- length
- width
- thickness
- All of above
- length
- width
- thickness
- All of above
- finite
- countless
- fixed
- All of above
- rail lines
- opposite edge of table
- opposite edge of ruler
- All of above
- length
- width
- no thickness
- All of above
- straight line
- curve
- plane
- None of these
- concurrent lines
- intersecting lines
- parallel lines
- transversal lines
- no end point
- one end point
- two end points
- three end points
- point of concurrence
- point of intersection
- collinear points
- mid point
- 00
- 1800
- 900
- 1200
