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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.

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

∙ A (read as point A)

∙ X (read as point X)

Two points A and X

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.

Example

$\stackrel{\⟷}{\mathrm{AB}}$

Line AB

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.

Example

$\stackrel{\⟶}{\mathrm{AB}}$

where, A is the starting fixed point of the ray.

Ray AB

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

$\stackrel{\u2014}{\mathrm{AB}}$

Line segment AB

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.

Example of a Plane

We can name the plane by using English alphabets. For example, the plane drawn in the above diagram can be named
with 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 of
a room.

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.

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

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 use
symbol ⊥.

So, we can write it as AB ⊥ CD or we can write as CD ⊥ AB.

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.

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 or CD||AB.

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.

Transversal lines AB and CD

Here, line AB cuts through two lines PQ and RS where line AB is called as **transversal line**.

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**.

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 the
**point of concurrence**.

A point is a mark of a position.

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

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

**Solution**

Ray is $\stackrel{\u27f6}{\mathrm{AC}}$

Line segment is $\stackrel{\u2014}{\mathrm{AB}}$

**Solution**

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

**Solution**

a. Parallel lines

b. Concurrent lines

c. Intersecting lines

d. Perpendicular lines

**Solution**

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

- 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

- 0
^{0} - 180
^{0} - 90
^{0} - 120
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