Points, Lines and Shapes

Definition of points, lines and shapes in geometry:

Point: A point is the fundamental element of geometry. If we put the tip of a pencil on a paper and press it lightly, we see a very small mark on the paper. This mark is known as a point.

The smallest mark denotes the existence of a point. We say that a point does not have any length, breadth or thickness, but it has a definite position.

It can be named by a capital letter of the English alphabet like A, B, C, ……. etc.

In short, we can make a small dot on a paper by using a sharp pencil or a tip of the needle. It is called a point. It represents a position and is marked by a capital letter A, B, C etc. A point has no size or shape. So, on a line an infinite number of points exist.

Points are generally use to tell the position of something and mark line-segments. A point is so small that it has to be drawn very carefully.

Solved Examples on Points:

1. How many points are marked in the given figure?

Solution:

There are 8 points marked in the figure i.e., A, B, C, D, E, F, G, H

Line: If two points are made at a distance on a surface and are joined by a pencil then a part of a line is formed. The part of the line will be straight if the surface is plane and curved if the surface is curved.

Thus, if we join any two points with a ruler and extend it on both sides, a line is formed.

A line is indicated by drawing arrow-heads on both sides of the part of a line.

The arrow-heads at the ends indicate that the line goes on in both directions. A line has no end, so it has not a definite length.

The name of a line is indicated by two capital letters of the English alphabet.

The symbol ↔ is placed over the letters as AB, CD.

These explanations on points, lines and shapes will help the kids to understand the different fundamental element of geometry and how they are indicated.

In short, a line is a straight path of points. A line has no beginning or end. A line is named by a single small letter l, m, n, etc. A line is also represented as \(\underset{AB}{\leftrightarrow}\). A line can be straight or curved.

SUMMARY:

• Line has no end points.

• It can be extended indefinitely in both directions.

• A line has no definite length.

• It is named A by a small letter of the English alphabet or two capital letters marked on it.

Straight Lines:

A line has no end points, it has no definite length.

Straight lines can be made in any direction.

\(\underset{XY}{\leftrightarrow}\) is a horizontal straight line.

\(\underset{CD}{\leftrightarrow}\) is a vertical straight line.

\(\underset{RS}{\leftrightarrow}\) is a slanting straight line.

We can call it oblique line.

Curved Lines:

Curved lines are fun lines and can be made anyway you like.

Line Segment:

The straight line between two points is called a line segment.

Here, PQ is a line segment.

The points P and Q are called the end points of the line segment PQ.

A line segment can be measured with a scale, i.e., it has a definite length.

It has no breadth or thickness.

Ray:

\(\overrightarrow{MN}\) is a ray. It has one arrowhead to show that it can be made longer from the side of N.

A ray \(\overrightarrow{MN}\) has one end point M. The point M is called the initial point of ray \(\overrightarrow{MN}\).

Intersecting Lines:

Lines \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) are crossing each other at a point P.

So, these are intersecting lines.

P is called the point of intersection.

Some examples of intersecting lines are letter 'X' and sign of addition'+'.

REMEMBER:

Symbols or sign

↔ stands for a straight line,

→ stands for a ray, and

― stands for a line segment.

Frequently asked questions on Points, Lines and Shapes in Geometry:

1. What is the definition of a point in math?

Answer:

A point gives an idea of a location by making a dot by a sharp pencil on a paper. It has no length, breadth and size. A point determines a location. A point has no dimension i.e., no shape or size.

For Example:

(i) The tip of a compass

(ii) The sharpened end of a pencil

(iii) The pointed end of a needle

2. How do you name a point?

Answer:

A point is denoted by a capital letter of the alphabet like A, B, C etc.

For Example:

These points will be read as 'point A. 'point B' and 'point C.

3. What is Definition of Line in Maths?

Answer:

A line is a straight path that extends indefinitely in both directions. It has no end points. It has neither breadth nor thickness.

For Example:

The straight crease formed by folding a piece of paper is a physical example which is quite close to the idea of a line. Other examples are the edge of a ruler, edges of a table, etc.

Worksheet on Definition of Points, Lines and Shapes:

1. Name the line segments in each of these figures.

Answer:

1. (i) PQ, QR, RS and SP

(ii) AB, BC, CD, DE and EA

2. Mark two points A and B on a sheet of paper. How many line segments can you draw passing through these points?

Answer:

2. one line

3. Fill in the blanks:

(i) A ray has __________ end point.

(ii) A line segment has __________ end points.

(iii) A line segment has __________ length.

(iv) A point shows a definite __________.

(v) A line MN is represented by __________.

Answer:

3. (i) one

(ii) two

(iii) definite

(iv) position

(v) \(\overleftrightarrow{MN}\)

Related Concepts

● Basic Shapes

● Surfaces of the Solids

● Common Solid Figures

● Line-Segment, Ray and Line

● Types of Lines

● Geometrical Design and Models

3rd Grade Math Lessons

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