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**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.

This Story also Contains

- 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

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.

- 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.

**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 Topic: Line Segment **

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

** 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.

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

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

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

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

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

(b) DB or BD

(c)

(d)

** 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.

(a) Line containing point E.

(b) Line passing through A.

(c) Line on which O lies

(d) Two pairs of intersecting lines.

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

(b) Line passing through A is AE.

(c) Line on which O lies is OC.

(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.

(a) Q, M, O, N, P are points on the line .

(b) M, O, N are points on a line segment .

(c) M and N are end points of line segment .

(d) O and N are end points of line segment .

(e) M is one of the end points of line segment .

(f) M is point on ray .

(g) Ray is different from ray .

(h) Ray is same as ray .

(i) Ray is not opposite to ray .

(j) O is not an initial point of .

(k) N is the initial point of and .

** Answer: ** (a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

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

** Answer: ** (a) Open

(b) Closed

(c) Open

(d) Closed

(e) Closed

** Q4 ** Consider the given figure and answer the questions :

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

** 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.

(c) A polygon with two sides.

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

e.g an ellipse or a circle

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

(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.

** Q1 ** Name the angles in the given figure.

Answer: The angles in the given figure are

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

(a) In the interior of

(b) In the exterior of

(c) On

** Answer: ** (a) Point A

(b) Points C, A and D

(c) Points E, B, O and F

** Q3 ** Draw rough diagrams of two angles such that they have

(a) One point in common.

(b) Two points in common.

(c) Three points in common.

(d) Four points in common.

(e) One ray in common.

** Answer: ** (a) and have point O in common.

(b) and have points O and B in common.

(c) and have points O, D and B in common.

(d) and have points O, D, E and B in common.

(e) and have ray in common

** 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.

** Answer: ** The sketch of the required triangle is as follows

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.

(c) Write the names of six line segments.

(d) Which two triangles have as common?

** Answer: ** (a) Three triangles in the given figure are , and .

(b) Seven angles in the given figure are , , , , , and .

(c) Six line segments in the given figure are AB, BC, CA, AD, BD and DC.

(d) and have as common.

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

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,

(c) two pairs of adjacent sides,

(d) two pairs of adjacent angles.

** Answer: ** The following is the sketch of a quadrilateral KLMN

(a) Two pairs of opposite sides are

(i) KL and MN.

(ii) LM and NK

(b) Two pairs of opposite angles are

(i) and

(ii) and

(c) Two pairs of adjacent sides are

(i) KL and LM

(ii) LM and MN

(d) Two pairs of adjacent angles are

(i) and

(ii) and

** Q1 ** From the figure, identify :

(a) the center of the circle

(b) three radii

(c) a diameter

(d) a chord

(e) two points in the interior

(f) a point in the exterior

(g) a sector

(h) a segment

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

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

(c) AC is a diameter 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.

(a) it's center

(b) a radius

(c) a diameter

(d) a sector

(e) a segment

(f) a point in its interior

(g) a point in its exterior

(h) an arc

** Answer: **

In the above-drawn circle

(a) O is the center of the circle.

(b) OR is a radius of the circle.

(c) PQ is a diameter 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.

(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. **

**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**

Chapters No. | Chapters Name |

Chapter - 1 | |

Chapter - 2 | |

Chapter - 3 | |

Chapter - 4 | Basic Geometrical Ideas |

Chapter - 5 | |

Chapter - 6 | |

Chapter - 7 | |

Chapter - 8 | |

Chapter - 9 | |

Chapter -10 | |

Chapter -11 | |

Chapter -12 | |

Chapter -13 | |

Chapter -14 |

- 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! *

1. What is the meaning of Geometry according class 6 chapter 4 maths?

Geometry has a long history. The 'Geometry' is the English equivalent of the Greek word 'Geometron'.

'Geo' means Earth and the 'Metron' means Measurement. thus according to chapter 4 maths class 6 geometry studies the sizes, shapes, positions, angles, and dimensions of things.

2. What is the largest chord of a circle?

The largest chord of a circle is called the diameter. The diameter is a chord that passes through the center of the circle and divides it into two equal halves. It is the longest possible chord in a circle and its length is twice the length of the radius. In other words, the diameter is the line segment that connects two points on the circle and passes through the center.

3. Please provide the definition of a polygon as described in NCERT Solutions for class 6 chapter 4 Maths.

As per the explanation provided in basic geometrical ideas class 6 worksheet with answers, a polygon is a closed shape formed by connecting line segments. Polygons come in various types, such as triangles (consisting of 3 line segments), quadrilaterals (consisting of 4 line segments), pentagons (consisting of 5 line segments), and so on.

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