# NCERT Solutions Class 6 Maths Chapter 4

## NCERT Solutions for Class 6 Mathematics Chapter 4

Practise questions given at the end of NCERT Book Class 6 are extremely useful for students, as they gauge their understanding of the chapter and help them score better marks in exams. However, students might find it difficult to solve the practise questions accurately, and this is where NCERT Solutions for Class 6 Mathematics Chapter 4 by Extramarks can be of great help.

## Basic Geometrical Concepts Class 6

Class 6 Mathematics Chapter 4 explains the concepts of points, line segments, lines, intersecting lines and other related topics in detail. The history of geometry is also discussed in the chapter.

### 4.1 Introduction

Students are introduced to the history of geometry as well as its applications in archeological departments and research.

### 4.2 Points

A point is the thinnest portion of your dot, and it establishes the location and helps point out some angle or another. As a result, students may understand the distinction between a dot and a point.

### 4.3 A Line Segment

A line segment has two endpoints. Students are explained the difference between a line and a line segment.

### 4.4 A line

Many students are perplexed by the difference between line and line segment if they lack a fundamental understanding of the concept. The NCERT book explains both the types with relevant pictures and details.

### 4.5 Intersecting Lines

Two lines meeting at a spot are called intersecting lines. The point of intersection is defined as the commonplace where two lines intersect.

### 4.6 Parallel Lines

Parallel lines have two lines that do not intersect and do not have a common point. The notions of intersecting lines and parallel lines should not be confused by students.

### 4.7 Ray

A ray is not a line or a piece of a line. Students should pay greater attention to geometry ideas because they appear identical but are very different. A ray is similar to an arc, but it lacks an ending.

### 4.8 Curves

Students will study the curve, which is not a straight line and does not intersect. It is simple to learn and to draw.

### 4.9 Polygons

Polygons are indefinite shapes produced by a set of line segments. The pattern can be anything you want, but the line segment is crucial.

### 4.10 Angles

In this section of Chapter 4, students will discover what an angle is, which is a broad topic in geometrical concepts.

### 4.11 Triangles

Triangles have three sides and three angles. Students are already familiar with this geometrical shape.

A quadrilateral has four sides and four angles.

### 4.13 Circles

A circle is a closed surface with some special properties. However, it is not a polygon.

### Key Takeaways of NCERT Solutions Class 6 Mathematics Chapter 4 Basic Geometrical Ideas

• NCERT Solutions by Extramarks are prepared by subject matter experts, hence students can count on these study materials for accuracy.
• All the answers are written in simple and easy-to-comprehend language.
• The solutions are prepared as per the latest guidelines by CBSE.
• The solutions can be accessed on the website and mobile app of Extramarks.

Q.1 Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments

Ans.

(a) Five points are: O, B, C, D and E.

$\left(\mathrm{b}\right)\text{A line is}\stackrel{↔}{\text{BD}}.$ 

$\left(\text{c}\right)\mathrm{}\text{Four rays are}:\stackrel{\to }{\mathrm{OB}},\stackrel{\to }{\mathrm{OE}},\stackrel{\to }{\mathrm{OD}},\stackrel{\to }{\mathrm{ED}}\text{and}\stackrel{\to }{\text{EB}}$

$\left(\text{d}\right)\text{Five line segments are}:\overline{\text{DE}},\text{}\overline{\text{EO}},\text{}\overline{\text{OB}},\text{}\overline{\text{EB}}\text{and}\overline{\text{DB}}.$

Q.2 Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Ans.

$Twelve ways to represent line are: AB ↔ , AC ↔ , AD ↔ , BC ↔ , BD ↔ , CD ↔ , DA ↔ , DB ↔ , DC ↔ , CB ↔ , CA ↔ MathType@MTEF@5@5@+=feaaguart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbwvMCKfMBHbqedmvETj2BSbqefm0B1jxALjhiov2DaerbuLwBLnhiov2DGi1BTfMBaebbnrfifHhDYfgasaacH8MrFz0xbba9q8WrFfeuY=Hhbbf9v8qqaqFr0xc9pk0xbba9q8WqFfea0=yr0RYxir=Jbba9q8aq0=yq=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@9903@$

Q.3 Use the figure to name:

(a) Line containing point E.
(b) Line passing through A.
(c) Line on which O lies
(d) Two pairs of intersecting lines.

Ans.

$\begin{array}{l}\left(\text{a}\right)\text{Line containing E is​}\stackrel{↔}{\text{AE}}\text{.}\\ \left(\mathrm{b}\right)\text{Line passing through A is}\stackrel{↔}{\text{AE}}\text{.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em} Line on which O lies is}\stackrel{↔}{\text{BC}}\text{.}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em} Two pairs of intersecting lines are:}\stackrel{↔}{\text{OC}}\text{and}\stackrel{↔}{\text{BE}},\text{}\stackrel{\to }{\text{AE}}\text{and}\stackrel{\to }{\text{EF}}.\end{array}$

Q.4 How many lines can pass through
(a) one given point?
(b) two given points?

Ans.

(a) Many lines can pass through one point.
(b) Only one line can pass through two given points.

Q.5

$\begin{array}{l}\mathrm{Draw}\mathrm{arough}\mathrm{figure}\mathrm{and}\mathrm{label}\mathrm{suitably}\mathrm{in}\mathrm{each}\mathrm{of}\mathrm{the}\\ \mathrm{following}\mathrm{cases}:\\ \left(\mathrm{a}\right)\mathrm{Point}\mathrm{P}\mathrm{lieson}\overline{\mathrm{AB}}.\\ \left(\mathrm{b}\right)\stackrel{↔}{\mathrm{XY}}\mathrm{and}\stackrel{↔}{\mathrm{PQ}}\mathrm{intersect}\mathrm{at}\mathrm{M}.\\ \left(\mathrm{c}\right)\mathrm{Line}\mathrm{l}\mathrm{contains}\mathrm{E}\mathrm{and}\mathrm{F}\mathrm{but}\mathrm{not}\mathrm{D}.\\ \left(\mathrm{d}\right)\stackrel{↔}{\mathrm{OP}}\mathrm{and}\stackrel{↔}{\mathrm{OQ}}\mathrm{meet}\mathrm{at}\mathrm{O}.\end{array}$

Ans.

(a)

(b)

(c)

(d)

Q.6

$\begin{array}{l}\mathrm{Consider}\mathrm{the}\mathrm{following}\mathrm{figure}\mathrm{of}\mathrm{line}\stackrel{↔}{\mathrm{MN}}.\mathrm{Say}\mathrm{whether}\\ \mathrm{following}\mathrm{statements}\mathrm{are}\mathrm{true}\mathrm{or}\mathrm{false}\mathrm{in}\mathrm{context}\mathrm{of}\mathrm{the}\\ \mathrm{given}\mathrm{figure}.\\ \left(\mathrm{a}\right)\mathrm{Q},\mathrm{M},\mathrm{O},\mathrm{N},\mathrm{Pare}\mathrm{points}\mathrm{on}\mathrm{the}\mathrm{line}\stackrel{↔}{\mathrm{MN}}.\\ \left(\mathrm{b}\right)\mathrm{M},\mathrm{O},\mathrm{N}\mathrm{are}\mathrm{points}\mathrm{on}\mathrm{a}\mathrm{line}\mathrm{segment}\stackrel{↔}{\mathrm{MN}}.\\ \left(\mathrm{c}\right)\mathrm{M}\mathrm{and}\mathrm{N}\mathrm{are}\mathrm{end}\mathrm{points}\mathrm{of}\mathrm{line}\mathrm{segment}\stackrel{↔}{\mathrm{MN}}.\\ \left(\mathrm{d}\right)\mathrm{O}\mathrm{and}\mathrm{N}\mathrm{are}\mathrm{end}\mathrm{points}\mathrm{of}\mathrm{line}\mathrm{segment}\overline{\mathrm{OP}}.\\ \left(\mathrm{e}\right)\mathrm{M}\mathrm{is}\mathrm{one}\mathrm{of}\mathrm{the}\mathrm{end}\mathrm{points}\mathrm{of}\mathrm{line}\mathrm{segment}\overline{\mathrm{QO}}.\\ \left(\mathrm{f}\right)\mathrm{M}\mathrm{is}\mathrm{point}\mathrm{on}\mathrm{ray}\stackrel{\to }{\mathrm{OP}}.\\ \left(\mathrm{g}\right)\mathrm{Ray}\stackrel{\to }{\mathrm{OP}}\mathrm{is}\mathrm{different}\mathrm{from}\mathrm{ray}\stackrel{\to }{\mathrm{QP}}.\\ \left(\mathrm{h}\right)\mathrm{Ray}\stackrel{\to }{\mathrm{OP}}\mathrm{is}\mathrm{same}\mathrm{as}\mathrm{ray}\stackrel{\to }{\mathrm{OM}}.\\ \left(\mathrm{i}\right)\mathrm{Ray}\stackrel{\to }{\mathrm{OM}}\mathrm{is}\mathrm{not}\mathrm{opposite}\mathrm{to}\mathrm{ray}\stackrel{\to }{\mathrm{OP}}.\\ \left(\mathrm{j}\right)\mathrm{O}\mathrm{is}\mathrm{not}\mathrm{an}\mathrm{initial}\mathrm{point}\mathrm{of}\stackrel{\to }{\mathrm{OP}}.\\ \left(\mathrm{k}\right)\mathrm{N}\mathrm{is}\mathrm{the}\mathrm{initial}\mathrm{point}\mathrm{of}\stackrel{\to }{\mathrm{NP}}\mathrm{and}\stackrel{\to }{\mathrm{NM}}.\end{array}$

Ans.

$\begin{array}{l}\left(\text{a}\right)\text{True},\text{Q},\text{M},\text{O},\text{N},\text{P are points on the line\hspace{0.17em}}\stackrel{↔}{\mathrm{MN}}.\\ \left(\mathrm{b}\right)\text{True},\text{M, O, N are points on a line segment}\stackrel{↔}{\text{MN}}\text{.}\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}True},\text{M and N are end points on a line segment}\stackrel{↔}{\text{MN}}\text{.}\\ \left(\mathrm{d}\right)\text{\hspace{0.17em}\hspace{0.17em}}\mathrm{False},\text{O and P are end points of line segment}\overline{\text{OP}}\text{.}\\ \left(\mathrm{e}\right)\text{\hspace{0.17em}}\mathrm{False},\text{Q and O are the end points of line segment}\overline{\text{OQ}}\text{.}\\ \left(\mathrm{f}\right)\text{\hspace{0.17em}}\mathrm{False},\text{N is a point of ray}\stackrel{\to }{\text{OP}}\text{.}\\ \left(\mathrm{g}\right)\text{True, both rays have different starting point.}\\ \left(\mathrm{h}\right)\text{}\mathrm{False},\text{both are opposite rays.}\\ \left(\mathrm{i}\right)\text{}\mathrm{False},\text{}\mathrm{ray}\stackrel{\to }{\mathrm{OM}}\mathrm{isoppositetoray}\stackrel{\to }{\mathrm{OP}}.\\ \left(\mathrm{j}\right)\text{\hspace{0.17em}}\mathrm{False},\text{O is initial point of}\stackrel{\to }{\mathrm{OP}}.\\ \left(\mathrm{k}\right)\text{True, N is initial point of both rays.}\end{array}$

Q.7 Classify the following curves as
(i) Open or
(ii)Closed.

Ans.

Q.8 Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve.

Ans.

Open curves are: (a) and (c).
Closed curves are: (b), (d) and (e).

Q.9 Draw any polygon and shade its interior.

Ans. The required pentagon is shaded as given below:

Q.10 Consider the given figure and answer the questions:
(a) Is it a curve?
(b) Is it closed?

Ans.

(a) Yes, it is a curve.
(b) Yes, it is closed.

Q.11 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.

Ans.

(a)

(b)

(c) A polynomial with two sides is not possible.

Q.12 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.

Point A is on the triangle ABC; it is neither in its exterior nor in its interior.

Q.13 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.

Diagonals are AC and BD. Meeting point of diagonals is in the interior of the quadrilateral.

Q.14 From the figure, identify:
(a) the centre of 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

Ans.

(a) O is the centre of the circle.
(b) Three radii are: OA, OB and OC.
(c) A diameter is AC.
(d) A chord is ED.
(e) Two points in the interior are: O and P.
(f) A point in the exterior is Q.
(g) OAB is a sector.
(h) EBD is a segment.

Q.15 (a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?

Ans.

(a) Yes, every diameter of a circle is also a chord.
(b) No, every chord of a circle is not a diameter.
Only a chord which passes through the centre of circle is called diameter.

Q.16 Draw any circle and mark
(a) its centre (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

Ans.

(a) Circle with centre O is given below:

(b) Circle with radius OA is given below:

(c) Circle with diameter AB is given below:

(d) Circle with sector AOB is given below:

(e) Circle with segment AB is given below:

(f) Point A is in the interior of circle is shown below:

(g) A point in its exterior of circle is shown below:

(h) An arc is shown below:

Q.17 Say true or false:
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.

Ans.

(a) True, two diameters of a circle will necessarily intersect.
(b) True, centre of a circle is always in its interior.

Q.18 Name the angles in the given figure.

Ans.

Four angles in the given figure are:
∠DAB, ∠ABC, ∠BCD and ∠CDA.

Q.19 In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF

Ans.

(a) Point A is in the interior of ∠DOE.
(b) Points A, C and D are in the exterior of ∠EOF.
(c) Points E, B, O and F lie on ∠EOF.

Q.20 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.

Ans.

(a) ∠ABC and ∠CBD have B as a common point.

(b) ∠ABC and ∠ABD have A and B as two common points.

(c) ∠ABC and ∠ACB have three common points.

(d) ∠DAC and ∠EPD have four common points i.e. B, C, D and E.

Q.21 (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 ∠B as common?

Ans.

(a) Three triangles are ΔABD, ΔADC and ΔABC.
(c) Six line segments are:

$\overline{\text{AB}},\text{}\overline{\text{AC}},\text{}\overline{\text{BD}},\text{}\overline{\text{DC}},\text{}\overline{\text{BC}}\text{and}\overline{\text{AD}}.$

(d) ΔABC and ΔABD have ∠B as common.

Q.22 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.

Ans.

(a) Two pairs of opposite sides are:
KL and MN, LM and KN.
(b) Two pairs of opposite angles are:
∠LKN and ∠LMN,
∠KLM and ∠KNM.
(c) Two pairs of adjacent sides are:
KL and LM, LM and MN.
(d) Two pairs of adjacent angles are:
∠LMN and ∠MNK,
∠KLM and ∠LMN.

1. Describe the circle and its components.

A circle differs from a polygon. It is a closed surface in which the starting point meets the ending point. A circle has various parts. The diameter is the line that splits it in half in the middle. The radius of the circle is half the diameter. Besides the diameter, chords refer to all the other lines dividing the circle into different segments.

2. Can I get the NCERT ebook for Class 6 Basic Geometrical Ideas?

Students can access the NCERT book for Class 6 Basic Geometrical Ideas on Extramarks. They can prepare for Class 6 Mathematics by practising geometry questions. Extramarks also provides NCERT Solutions for Chapter 4 to help students solve NCERT textbook questions.

3. What are the fundamental geometrical concepts?

Geometry aids us in determining how shapes and figures fit together, maximising efficiency, and improving visual attractiveness. Basic geometrical concepts include basic geometrical shapes such as circles, lines, triangles, quadrilaterals, curves, polygons and angles. It also helps us understand the basic definitions and differences of vertices and edges along with different types of vertical edges. Various triangular pyramid properties, volume face edges, to calculate height width and square feet, congruence and rays, among others can also be understood by fundamental geometrical concepts.