Maharashtra Board Class 6 Maths part 1 Chapter 1 Basic Concepts in Geometry PDF Download

Part One: Basic Concepts In Geometry

Points

A point is shown by a tiny dot. We can use a pen or a sharp pencil to make the dot. The dots in the rangoli are the symbols for points.

A point can be given a name. Capital letters of the alphabet are used to name a point. The points P, A and T are shown in the figure alongside.

Teacher's Note

When you make a rangoli at home, each small dot is a point. Just like we name things with capital letters, points also have names like A, B, and C.

Exam Trick

Remember: A point has NO size. It is just a dot. You cannot measure it. Think of it like a star in the sky - it looks small but it is really far away.

Points to Remember

A point is a tiny dot made with a pen or pencil.
Points are named using capital letters like A, B, C.
A point has no length, width, or height.
We use dots in rangoli to show points.

Line Segments and Lines

Take two points A and B on a sheet of paper and join them using a ruler. We get the straight line AB. Can we extend this line further on the side of point B? On the side of point A? How far can we extend it?

We can extend the line in both directions till the edges of the paper. If the paper is very big, the line can be very long, too.

How long would the line be on a playing field?

Let us imagine that we can extend this line forever without any limits on both sides. To show this extended line on paper, we use arrowheads at both ends of the line. In mathematics, when we say line, we mean 'straight line'. The first line that we drew was only from point A to point B. It was a piece or a segment of the longer line.

A line segment has two points showing its limits. They are called endpoints. We write line segment AB as 'seg AB' in short. A and B are its endpoints. A line is named using a small letter or by using any two points on the line. Line l has been shown alongside. Its name can also be written as line PQ or line QP.

Teacher's Note

When you draw a line on paper from one point to another, that is a line segment. But imagine that line going on and on forever - that is a line. A line has no end.

Exam Trick

Remember: Line segment = has two endpoints like AB. Line = goes forever with arrows at both ends. Segment has limits, line does not.

Points to Remember

A line segment is a straight line between two points.
The two points of a line segment are called endpoints.
A line goes on forever in both directions.
We use arrows to show that a line continues forever.
We write line segment AB as seg AB.

Rays

Look at the pictures. What do you see? Rays starting from the sun go forward in all directions. Light rays from the torch also start from a point and go forward continuously in one direction.

A ray is a part of a line. It starts at one point and goes forward continuously in the same direction. The starting point of a ray is called its origin. Here, P is the origin. An arrowhead is drawn to show that the ray is infinite in the direction of Q. The figure can be read as ray PQ.

The ray PQ is not read as ray QP.

Activity 1: Draw a point on the blackboard. Every student now draws a line that passes through that point. How many such lines can be drawn?

Activity 2: Draw a point on a paper and use your ruler to draw lines that pass through it. How many such lines can you draw?

An infinite number of lines can be drawn through one point.

When two or more lines pass through the same point, they are called concurrent lines and the common point through which they pass is called their point of concurrence. In the figure alongside, which is the point of concurrence? Name it.

Teacher's Note

A ray is like light coming from the sun. It starts from one point and keeps going. A torch light is also a ray - it starts from the torch and goes forward only.

Exam Trick

Remember: Ray = starts at one point and goes forever in ONE direction. It has an arrow on one side only. Ray PQ and ray QP are different.

Points to Remember

A ray starts at one point and goes forever in one direction.
The starting point of a ray is called the origin.
We draw an arrow to show the ray continues forever.
Ray PQ is different from ray QP.
Many lines can pass through one point.

Planes

Look at the pictures. What kind of surfaces do you see? The surfaces in the first two pictures are flat. Each flat surface is a part of an infinite surface. In mathematics, a flat surface is called a plane.

The name of the plane in the picture is 'H'. Even though we draw a suitably small figure of the plane, it actually extends infinitely on all sides. Arrows are drawn to show that the plane extends infinitely in all directions. However, these arrows are often omitted for the sake of convenience.

There are 9 points in this figure. Name them.

If you choose any two points, how many lines can pass through the pair?

One and only one line can be drawn through any two distinct points.

Which three or more of these nine points lie on a straight line? Three or more points which lie on a single straight line are said to be collinear points. Of these nine points, name any three or more points which do not lie on the same line. Points which do not lie on the same line are called non-collinear points.

Teacher's Note

A plane is any flat surface. Your notebook page is a plane. Your classroom floor is a plane. A plane has no thickness and goes on forever in all directions.

Exam Trick

Remember: Collinear = on the same line. Non-collinear = not on the same line. Think: co = same, so collinear = on same line.

Points to Remember

A plane is a flat surface that goes on forever in all directions.
Collinear points are points that lie on the same straight line.
Non-collinear points do not lie on the same straight line.
Only one line can pass through any two different points.
We can name a plane using a capital letter like H.

Parallel Lines

Look at this page from a notebook. Is this page a part of a plane? If we extend the lines that run sideways on the page, will they meet each other somewhere?

Lines which lie in the same plane but do not intersect are said to be parallel to each other.

Teacher's Note

The lines on your notebook page are parallel. The railway tracks are parallel. They never meet no matter how far you go. That is why trains can run on them safely.

Exam Trick

Remember: Parallel lines = same plane + never meet. Like two railway tracks side by side, they go on forever but never touch.

Points to Remember

Parallel lines lie in the same plane.
Parallel lines never meet or intersect.
Parallel lines are always the same distance apart.
The lines on notebook pages are examples of parallel lines.
We can extend parallel lines forever and they still will not meet.

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