Learn Point, Line, Ray & Plane With Free Worksheets

A point and a line are the most fundamental building blocks to make shapes in geometry.

This chapter discusses the definitions and examples of point, line, ray, line segment, plane and how two or more than two lines meet at a point for example the intersecting lines, perpendicular lines, parallel lines, transversal lines and concurrent lines with the help of diagrams.

Point

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.

Example of points

∙ A (read as point A) and ∙ X (read as point X)

Line

A Line is a one dimensional figure which is straight, has indefinite length and no thickness. Lines can be extended indefinitely but 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 of line

$\overset{\leftrightarrow}{A B}$ is a line.

Ray

It is a straight line which starts from one fixed point and always progresses 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.

Example of ray

$\vec{A B}$ is a ray and A is the fixed starting point.

Line segment

A Line segment is a part or segment of a line that is bounded by two distinct end points that 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.

The line segment is also represented by two capital letters of alphabets but with a line on top of it.

Example of line segment

$\overset{━}{A B}$ is the line segment.

Line segment AB with two end points A and B

Plane in geometry

In geometry, a plane is a flat and smooth surface. It has length and width. It has no thickness. Planes can be extended indefinitely in all directions.

The real life examples of a plane that we can see around us are the surface of a wall and ceiling of a room.

We can name the plane by using English alphabets.

Examples of planes

The plane drawn in the diagram is named with letters A, B and C and called plane ABC.

This plane can be named plane PQRS with letters P, Q, R and S.

Intersecting lines

Two lines are said to be intersecting lines if they meet out at a point.

Example of intersecting lines

In the figure AB and CD are the Intersecting lines. AB and CD intersect each other at a point E.

Perpendicular lines

The lines are said to be perpendicular lines if they intersect each other and the angle between them is 90°.

Example of perpendicular lines

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.

Lines AB and CD intersecting at O at 90°

Parallel lines

Two straight lines are said to be parallel lines if they do not intersect each other at any point and can be extended in both directions indefinitely.

Example of parallel lines

Line AB is parallel to CD. To denote it, we can use symbol ||. So. it is written as AB||CD or CD || AB.

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.

Example of parallel lines

AB cuts through two lines PQ and RS, the line AB is called transversal line.

Transversal lines AB intersecting parallel lines PQ and RS

Concurrent lines

If three or more straight lines pass through the same point or intersect each other at the same point, then these lines are called concurrent lines. The point where lines intersect each other, is called point of concurrence.

Example of concurrent lines

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.

Concurrent lines AB, CD, PQ and RS intersecting each other at T

What are collinear points?

If three or more points lie on the same straight line then points are called collinear points.

Example of collinear lines

Here, A, B, C and D are collinear points as they lie in the same straight line.

Collinear points A, B, C and D on a line

Learn Frequently Asked Questions

What is a point in geometry?

A point is a mark of a position.

What is a line?

A line refers to a straight line which can be extended indefinitely in both directions.

What is a plane?

A plane is a flat surface which can be extended indefinitely in all directions.

Practice With Solved Examples

Identify ray and line segments from the following figure.

Ray is $\vec{A C}$

Line segment is $\overset{━}{A B}$

Draw a line m and name a line segment AB on line m.

Here, m is a line and AB is a line segment on it.

Check whether the following pairs of lines are parallel, intersecting, concurrent or perpendicular?

Solutions:

Parallel lines
Concurrent lines
Intersecting lines
Perpendicular lines

How many line segments are there in the following figure?

PQ, PR, PS, QR, QS and RS are six line segments.

Fill in Blanks Worksheet

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.