# NCERT Class 6 Maths Chapter 4 ‘Basic Geometrical Ideas’: Notes and Solutions (Free PDF)

In this chapter, students will understand the concept of geometrical shapes and their properties. The students will get to know about the points, line segments, lines, intersecting lines, parallel lines, rays, polygons and many more shapes. Read through for CBSE Class 6 NCERT Maths Chapter 4 Basic Geometrical Ideas Notes, Exercise and Important Questions.

## CBSE Class 6 NCERT Maths Chapter 4 Basic Geometrical Ideas Notes – Free PDF Download

Below we have given topic-wise notes for the CBSE Class 6 NCERT Maths Chapter 4 Basic Geometrical Ideas. We have also provided a downloadable free PDF at the end of these notes so you can download and take a printout to study later when you need quick revision before going to the exam hall.

Also Read: Different Branches of Mathematics

### Topic 1: Points

• Point: A point determines a location. If you mark three points on a paper, you will be required to distinguish them. For this, they are denoted by a single capital letter like A, B, and C.

### Topic 2: Line Segment

• Line Segment: A line with a definite length, i.e. it has two endpoints on either end is called a line segment. The two endpoints, say A and B (including A and B) denote the line segment by AB or BA with a (–) on top.

### Topic 3: Line

• Line: A line has no endpoints and has an infinite number of points. A line through points A and B can be represented as AB with a (↔) on top.

### Topic 4: Intersecting Lines

• Intersecting Lines: Two lines having a common point are called intersecting lines.

For eg, let us consider two lines l1 and l2 intersecting at a point P will be represented as:

### Topic 5: Parallel Lines

• Parallel Lines: Lines that do not have a common point or the lines that do not meet are called parallel lines.

For eg, the lines A, B and C given below are parallel lines.

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### Topic 6: Ray

• Ray: A ray is a portion of a line, it starts at one point (called a starting point) and goes endlessly in a direction.

### Topic 7: Curves

• Curves: Curve’ in everyday usage means “not straight”. If a curve does not cross itself, then it is called a simple curve.
• Open Curve: When a curve does not make a closed shape.
• Closed Curve: When a curve makes a closed shape/figure.

### Topic 8: Polygons

• Polygons: Any closed shape formed solely by line segments is called Polygons.

For eg,

• Sides: The line segments forming a polygon are called its sides.
• Vertices: The meeting point of a pair of sides is called its vertex.
• Diagonal: Consider the pairs of vertices which are not adjacent. The joins of these vertices are called the diagonals of the polygon.

### Topic 9: Angles

• Angles: Angles are made when corners are formed. Note that in specifying the angle, the vertex is always written as the middle letter.

For eg, the angle formed by rays OP and OQ is ∠POQ.

### Topic 10: Triangles

• Triangles:  A triangle is a three-sided polygon.

• Quadrilaterals: A four-sided polygon is a quadrilateral. It has 4 sides and 4 angles.

### Topic 12: Circles

• Circles: A circle is a simple closed curve which is not a polygon. It has some very special properties.
• Radius: The radius is a line segment that connects the centre to a point on the circle. It is represented by “r”.
• Diameter: A line segment passing through the centre of a circle and connecting to either side is called the diameter. For a given circle, the diameter is double the length of the radius of the circle, i.e. d = 2r.

## Important Questions in NCERT Class 6 Maths Chapter 4: Free PDF Download

Below we have provided some important exercise questions and their solutions from Chapter 4 of CBSE NCERT Maths for Class 6.

### Exercise 4.1

Q 1. Name the line given in all possible (twelve) ways, choosing only two letters at a

time from the four given.

Ans. The names of the line in all the twelve possible ways are:

Q 2. How many lines can pass through (a) one given point? (b) two given points?

1. Infinite numbers of lines can pass through 1 given point.
2. Only 1 line can pass through 2 given points.

Q 3. Consider the following figure of line MN. Say whether the following statements are true or false in the context of the given figure.

1. Q, M, O, N, P are points on the line MN.
2. M, O, N are points on a line segment MN .
3. M and N are end points of line segment MN .
4. O and N are end points of line segment OP .
5. M is one of the end points of line segment QO .
6. M is point on ray OP.

1. True
2. True
3. True
4. False
5. False
6. False

### Exercise 4.2

Q 1.  Draw any polygon and shade its interior.

Ans. The below given figure is a polygon with its centre shaded.

Q 2.  Consider the given figure and answer the questions :

1. Is it a curve?
2. Is it closed?

Ans. Let us see each statement below.

1. All the lines are connected in the given figure, making it a closed curve. Hence, yes, the given figure is a closed curve.
2. Yes, it is a closed curve.

Q 3.  Illustrate, if possible, each one of the following with a rough diagram:

1. A closed curve that is not a polygon.
2. An open curve made up entirely of line segments.
3. A polygon with two sides.

Ans. The illustrations in each case are given below.

1. A polygon requires a minimum of 3 line segments. So, it is not possible to form a polygon with 2 sides.

Also Read: Multiplication and Division Word Problems

### Exercise 4.3

Q 1.  In the given diagram, name the point(s)

1. In the interior of ∠DOE
2. In the exterior of ∠EOF
3. On ∠EOF

1. The point in the interior of the ∠DOE is A.
2. The points in the exterior of the ∠EOF are C, A and D.
3. The points on the ∠EOF are E, B, O and F.

### Exercise 4.4

Q 1.  Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?

Ans. The point A is neither in the interior nor in the exterior of the triangle. The point lies on the triangle.

### Exercise 4.5

Q 1. Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?

Ans. The meeting point O of the diagonals PR and QS of the quadrilateral PQRS lie in the interior of the quadrilateral.

### Exercise 4.6

Q 1.  From the figure, identify :

1. the centre of circle

Q 2. Is every diameter of a circle also a chord?

Ans. Yes, every diameter of a circle is also a chord. The diameter is called the longest chord in a circle.

Q 3. Say true or false:

1. Two diameters of a circle will necessarily intersect.
2. The centre of a circle is always in its interior.

1. True. The diameter of a circle passes through the centre. So, yes, two diameters will necessarily intersect.
2. True

Also See:

CBSE NCERT Class 6 Maths Chapter 1 Knowing Our Numbers Notes and Important Questions – Free PDF

CBSE NCERT Class 6 Maths Chapter 2 Whole Numbers Notes, Exercise and Important Questions – Free PDF

CBSE NCERT Class 6 Maths Chapter 3 Playing With Numbers, Exercise and Important Questions – Free PDF

## FAQs

Q.1. What is a circle?

Ans: A circle is a simple closed curve which is not a polygon.

Q.2. How are angles formed?

Ans: Angles are made when corners are formed. Note that in specifying the angle, the vertex is always written as the middle letter.

Q.3. What is a Ray?

Ans: A ray is a portion of a line, it starts at one point (called a starting point) and goes endlessly in a direction.

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