NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Updated on Nov 29, 2023 05:17 PM IST

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas are discussed here. These NCERT solutions are prepared by subjects matter expert at careers360 keeping in my the latest CBSE syllabus 2023. This NCERT Class 6 solution for chapter 4 will introduce figures like- triangle, quadrilaterals, circles, polygon, regular polygon, etc, which you often observe in your day-to-day lives. NCERT solutions for Class 6 Maths chapter 4 Basic Geometrical Ideas covers the solutions of all these kinds of shapes. In this particular chapter of NCERT, you will learn more about the shapes around us. NCERT Class 6 solution for chapter 4 Basic Geometrical Ideas will help in creating a foundation of geometry for the upcoming classes.

Latest: Important Maths Formulas for Class 6 - Chapterwise

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NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas - Important Formula
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas - Important Points
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas (Intext Questions and Exercise)
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.1
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.2
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.3
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.4
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.5
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.6

$NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas$

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Before going through the Class 6 Maths NCERT solutions, check the NCERT Syllabus for Class 6 Maths to get the basic outline of the topics. CBSE NCERT solutions for Class 6 Maths chapter 4 is created to help you when you are while you. This chapter is having a total of 23 questions in 6 exercises. NCERT solutions for Class 6 Maths chapter 4 Basic Geometrical Ideas are covering all the questions' solutions given in the NCERT Books for Class 6 Maths. Along with Class 6 NCERT solution for Maths chapter 4, you can take a look at.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas - Important Formula

Line segments are the shortest distance between two points.
They are represented by a straight line connecting two specific points, denoted as AB
When two distinct lines meet at a common point, they are called intersecting lines.
Parallel lines are lines that will never intersect each other.
A polygon is a closed figure made up of different line segments.
Any two sides of a polygon that share a common endpoint are called adjacent sides.
The point where a pair of sides meet in a polygon is called a vertex.
Vertices that are located on the same sides of a polygon are called adjacent vertices.
A diagonal is a line segment that connects the endpoints of two non-adjacent vertices in a polygon.
A quadrilateral is a polygon with four sides.
In a quadrilateral ABCD, sides AB and CD are pairs of opposite sides.
Similarly, sides BC and AD are pairs of opposite sides.
In a quadrilateral ABCD, angles ABC and CDA are pairs of opposite angles.
Similarly, angles BCD and DAB are pairs of opposite angles.
Angle BCD is adjacent to angles ABC and CDA.
Similar relations hold for the other three angles in the quadrilateral.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas - Important Points

Point: A point is a fundamental geometric concept that represents a location in space. It has no size, shape, or dimensions and is usually denoted by a capital letter.

Line Segment: A line segment is a part of a line that connects two distinct points. It is the shortest distance between the two points and is represented by the two endpoints denoted as AB, where A and B are the endpoints.

Line: A line is formed by extending a line segment infinitely in both directions. It has no endpoints and continues indefinitely. A line is denoted by using the two endpoints of a line segment, such as AB, or sometimes represented by a single small letter like 'l'.

Intersecting Lines: When two distinct lines meet or cross at a single point, they are called intersecting lines. The point at which they intersect is known as the point of intersection.

Parallel Lines: Two lines in a plane are said to be parallel if they do not intersect, even when extended indefinitely. Parallel lines never meet and remain equidistant from each other at all points.

Ray: A ray is a portion of a line that starts from a point (called the endpoint) and extends infinitely in one direction. It has only one endpoint but goes on indefinitely in the other direction.

Curve: In geometry, a curve refers to any continuous and smooth line, whether straight or non-straight, that can be drawn without lifting the pencil. In this context, a line is also considered a curve.

Simple Curve: A simple curve is a curve that does not intersect or cross itself. It is a smooth and continuous curve without any self-intersections.

Closed Curve: A closed curve is a curve whose ends are joined, forming a complete loop or shape without any openings. It creates a boundary that encloses a region. In contrast, an open curve does not have its ends connected.

Polygon: A polygon is a simple closed curve made up of line segments. It is a two-dimensional geometric figure with straight sides. The properties of a polygon include:

(i) Sides: The line segments that form the polygon are called sides.

(ii) Adjacent Sides: Any two sides that share a common endpoint are called adjacent sides.

(iii) Vertex: The meeting point of two sides is called a vertex (plural: vertices).

(iv) Adjacent Vertices: The endpoints of the same side are known as adjacent vertices.

(v) Diagonal: The line segment that joins any two non-adjacent vertices of a polygon is called a diagonal.

Angle: An angle is formed by two rays that share a common initial point. The rays are referred to as the sides of the angle, and the common initial point is called the vertex of the angle. The angle is denoted by the three-letter notation, where the vertex is mentioned in the middle (e.g., ∠AOB or ∠BOA).

An angle divides the space around it into three regions:

Angle Itself: The actual measurement between the two rays that form the angle.

Interior of the Angle: The region enclosed by the angle's sides.

Exterior of the Angle: The region outside the angle but within the plane.

Free download NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas PDF for CBSE Exam

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

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NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Topic: Line Segment

Q1 Name the line segments in the figure. Is A, the endpoint of each line segment?

1643036777918

Answer: The line segments in the figure are BA and AC.

A is one of the endpoints of both BA and AC.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Topic: Ray

Q1 Name the rays given in this picture.

1643036825562

Answer: The rays given in this picture are TA and TB.

Q2 Is T a starting point of each of these rays?

1643036854366

Answer: Yes. T is the starting point of each these rays.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.1

Q1 Use the figure to name :

(a) Five points

(b) A line

(d) Five line segments

1643036887152

Answer: (a) D, E, O, B and C

(b) DB or BD

(d) $\bar{O E}, \bar{O D}, \bar{O B}, \bar{D E} a n d \bar{E B}$

Q2 Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

1643036915673

Answer: The given line can be named in the following 12 ways.

AB, BA, AC, CA, AD, DA, BC, CB, BD, DB, CD and DC.

Q3 Use the figure to name :

(a) Line containing point E.

(b) Line passing through A.

(d) Two pairs of intersecting lines.

1643036946307

Answer: (a) Line containing point E is DE or FE.

(b) Line passing through A is AE.

(d) Two pairs of inter secting lines are

(i) CO and AE

(ii) AE and EF

Q4 How many lines can pass through

(a) one given point?

(b) two given points?

Answer: (a) Infinite lines can pass through a given point.

(b) Only one line can pass through two given points.

Q5 (a) Draw a rough figure and label suitably in each of the following cases: Point P lies on $\overset{―}{A B}$ .

Answer: (a) 1643036981632

Q5 (b) Draw a rough figure and label suitably in each of the following cases: $\overset{―}{X Y}$ and $\overset{―}{P Q}$ intersect at M.

Answer: (b) 1643037009842

Q5 (c) Draw a rough figure and label suitably in each of the following cases: Line $l$ contains E and F but not D.

Answer: (c) 1643037036789

Q5 (d) Draw a rough figure and label suitably in each of the following cases: $\overset{―}{O P}$ and $\overset{―}{O Q}$ meet at O.

Answer: (d) 1643037064950

Q6 Consider the following figure of line $\overset{―}{M N}$ . Say whether following statements are true or false in context of the given figure.

(a) Q, M, O, N, P are points on the line $\overset{―}{M N}$ .

(b) M, O, N are points on a line segment $\overset{―}{M N}$ .

(d) O and N are end points of line segment $\overset{―}{O P}$ .

(e) M is one of the end points of line segment $\overset{―}{Q O}$ .

(f) M is point on ray $\vec{O P}$ .

(g) Ray $\vec{O P}$ is different from ray $\vec{Q P}$ .

(h) Ray $\vec{O P}$ is same as ray $\vec{O M}$ .

(i) Ray $\overset{―}{O M}$ is not opposite to ray $\overset{―}{O P}$ .

(j) O is not an initial point of $\overset{―}{O P}$ .

(k) N is the initial point of $\overset{―}{N P}$ and $\overset{―}{N M}$ .

1643037103732

Answer: (a) True

(b) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.2

Q1 Classify the following curves as (i) Open or (ii) Closed

sunny

Answer: (a) Open

(b) Closed

(d) Closed

(e) Closed

Q2 Draw rough diagrams to illustrate the following :

(a) Open curve (b) Closed curve.

Answer: (a) 1643037137819

(b) 1643037153676

Q3 Draw any polygon and shade it is interior.

Answer: Polygon ABCDEF

Q4 Consider the given figure and answer the questions :

(a) Is it a curve? (b) Is it closed?

1643037232833

Answer: (a) Yes it is a curve.

(b) Yes it is closed.

Q5 Illustrate, if possible, each one of the following with a rough diagram:

(a) A closed curve that is not a polygon.

(b) An open curve made up entirely of line segments.

Answer: (a) A closed curve that is not a polygon is possible.

e.g an ellipse or a circle

1643037261692

(b) An open curve made up entirely of line segments

1643037273290

(c) A polygon with two sides is not possible since by definition polygons are closed figures which require at least three line segments to be made.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.3

Q1 Name the angles in the given figure.

1643037299610

Answer: The angles in the given figure are $∠ A B C, ∠ B C D, ∠ C D A a n d ∠ D A B$

Q2 In the given diagram, name the point(s)

(a) In the interior of $∠ D O E$

(b) In the exterior of $∠ E O F$

1643037332373

Answer: (a) Point A

(b) Points C, A and D

Q3 Draw rough diagrams of two angles such that they have

(a) One point in common.

(b) Two points in common.

(d) Four points in common.

(e) One ray in common.

Answer: (a) $∠ A O B$ and $∠ C O D$ have point O in common.

1643037368909

(b) $∠ A O B$ and $∠ B O C$ have points O and B in common.

1643037379630

1643037391312

(d) $∠ A O B$ and $∠ B O C$ have points O, D, E and B in common.

1643037403217

(e) $∠ A O B$ and $∠ B O C$ have ray $\vec{O B}$ in common

1643037413965

Note: You will find the solutions at many sites saying that the angles required in (c) and (d) is not possible but that will be the case only if it is mentioned that the common points have to be on different rays.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.4

Q1 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?

Answer: The sketch of the required triangle is as follows

1643037443316

Point A is neither in the interior or the exterior of the triangle ABC. It is a vertex.

Q2 (a) Identify three triangles in the figure.

(b) Write the names of seven angles.

(d) Which two triangles have $∠ B$ as common?

1643037496179

Answer: (a) Three triangles in the given figure are $Δ A B D$ , $Δ A C D$ and $Δ A B C$ .

(b) Seven angles in the given figure are $∠ A B D$ , $∠ B D A$ , $∠ D A B$ , $∠ A D C$ , $∠ D C A$ , $∠ C A D$ and $∠ B A C$ .

(d) $Δ A B D$ and $Δ A B C$ have $∠ B$ as common.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.5

Q1 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?

Answer: Sketch of the required quadrilateral PQRS is as follows.

1643037524720

Its diagonals are PR and QS which meet at the point O. The meeting point of the diagonals O is in the interior of the quadrilateral.

Q2 Draw a rough sketch of a quadrilateral KLMN. State,

(a) two pairs of opposite sides,

(b) two pairs of opposite angles,

(d) two pairs of adjacent angles.

Answer: The following is the sketch of a quadrilateral KLMN

1643037554060

(a) Two pairs of opposite sides are

(i) KL and MN.

(ii) LM and NK

(b) Two pairs of opposite angles are

(i) $∠ K L M$ and $∠ M N K$

(ii) $∠ L M N$ and $∠ N K L$

(i) KL and LM

(ii) LM and MN

(d) Two pairs of adjacent angles are

(i) $∠ K L M$ and $∠ L M N$

(ii) $∠ N K L$ and $∠ M N K$

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.6

Q1 From the figure, identify :

(a) the center of the circle

(b) three radii

(d) a chord

(e) two points in the interior

(f) a point in the exterior

(g) a sector

(h) a segment

1643037588485

Answer: (a) O is the centre of the circle.

(b) OA, OB and OC are three radii of the circle.

(d) ED is a chord of the circle.

(e) Points O and P are in the interior of the circle.

(f) Point Q is a point in the exterior of the circle.

(g) The shaded region OAB is a sector of the circle.

(h) The shaded region EDE is a segment of the circle.

Q2 (a) Is every diameter of a circle also a chord?

(b) Is every chord of a circle also a diameter?

Answer: (a) Yes, every diameter of a circle is also a chord.

(b) No, not every chord of a circle is a diameter.

Q3 Draw any circle and mark

(a) it's center

(b) a radius

(d) a sector

(e) a segment

(f) a point in its interior

(g) a point in its exterior

(h) an arc

Answer:

1643037625824

In the above-drawn circle

(a) O is the center of the circle.

(b) OR is a radius of the circle.

(d) Shaded region OSQ is a sector of the circle.

(e) Shaded region ABC is a segment of the circle.

(f) K is a point in the interior of the circle.

(g) L is a point in the exterior of the circle.

(h) UV is an arc of the circle.

Q4 Say true or false :

(a) Two diameters of a circle will necessarily intersect.

(b) The center of a circle is always in its interior.

Answer: (a)Two diameters of a circle will necessarily intersect - True.

(b) The center of a circle is always in its interior- True.

Key Features Of Basic Geometrical Ideas Class 6 Maths Chapter 4

Comprehensive Coverage: The maths class 6 chapter 4 provides a comprehensive coverage of basic geometric concepts, ensuring a thorough understanding of fundamental ideas in geometry.

Structured Learning: The NCERT solutions for class 6 maths chapter 4 is organized in a structured manner, introducing concepts gradually and building upon previous knowledge. This allows for a step-by-step understanding of geometric ideas.

Clear Explanations: The chapter offers clear explanations of geometric terms and concepts, making it easier for students to grasp and apply them.

Also Check

NCERT Books and NCERT Syllabus

NCERT Solutions for Class 6 Mathematics - Chapter Wise

Chapters No.	Chapters Name
Chapter - 1	Knowing Our Numbers
Chapter - 2	Whole Numbers
Chapter - 3	Playing with Numbers
Chapter - 4	Basic Geometrical Ideas
Chapter - 5	Understanding Elementary Shapes
Chapter - 6	Integers
Chapter - 7	Fractions
Chapter - 8	Decimals
Chapter - 9	Data Handling
Chapter -10	Mensuration
Chapter -11	Algebra
Chapter -12	Ratio and Proportion
Chapter -13	Symmetry
Chapter -14	Practical Geometry

NCERT Solutions for Class 6 - Subject Wise

NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Science

How to Use NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas?

Try to relate all the figures with the things around us.
Learn the concepts given related to a particular figure.
Take a look through some examples to understand the application of those concepts.
Solve the unsolved problems given in the practice exercises.
While solving the unsolved questions if you stuck anywhere you can take the help of NCERT Solutions for Class 6 .

Keep working hard always and happy learning!

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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

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NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas - Important Formula

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas - Important Points

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas (Intext Questions and Exercise)

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.1

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.2

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.3

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.4

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.5

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise: 4.6

Key Features Of Basic Geometrical Ideas Class 6 Maths Chapter 4

NCERT Solutions for Class 6 Mathematics - Chapter Wise

NCERT Solutions for Class 6 - Subject Wise

How to Use NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas?

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