Basic Geometrical Concept Class-6 ML Aggarwal ICSE Mathematics Chapter-10 Solutions. We provide step by step Solutions of Exercise / lesson-10 Basic Geometrical Concept ICSE Class-6th ML Aggarwal Mathematics.

Our Solutions contain all type Questions with Exe- 10.1, Exe-10.2, Exe-10.3,  Exe-10.4 , Objective Type Questions  (includes: Mental Maths, Multiple Choice Questions , HOT ) and Check Your Progress  to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-6 Mathematics.

## Basic Geometrical Concept Class-6 ML Aggarwal ICSE Mathematics Chapter-10 Solutions

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Exercise 10.1 ,

Exercise-10.2,

Exercise-10.3,

Exercise-10.4,

Objective Type Questions,

Mental Maths,

Multiple Choice Questions ,(MCQ)

HOTS

### Exercise-10.1, Basic Geometrical Concept Class-6 ML Aggarwal ICSE Mathematics Solutions

#### Question 1

How many lines can be drawn through a given point?

Unlimited number of lines.

#### Question 2.

How many lines can be drawn through two distinct given points?

One

#### Question 4

Mark three non-collinear points A, B and C in your note-book. Draw lines through these points taking two at a time and name these lines. How many such different lines can be drawn?

#### lines AB, BC and CA; three.

Question 5.
Use the figure to name :
(i) Five point
(ii) Aline
(iii) Four rays
(iv) Five line segments

(i) O, B, C, D, E
(ii) $\overleftrightarrow { DE, } \overleftrightarrow { DO } ,\overleftrightarrow { DB, } \overleftrightarrow { EO } ,$ etc.
(iii) $\overleftrightarrow { DB } ,\overleftrightarrow { DE } ,\overleftrightarrow { OB } ,\overleftrightarrow { OE } ,\overleftrightarrow { EB, }$ etc.
(iv) $\overline{\mathrm{DE}}, \overline{\mathrm{DO}}, \overline{\mathrm{EO}}, \overline{\mathrm{OB}}, \overline{\mathrm{EB}}$, etc.

#### Question 6

Use the figure to name:

(i) Line containing point E.
(ii) Line passing through A.
(iii) Line on which point O lies.
(iv) Two pairs of intersecting lines.

#### (i) $\overleftrightarrow { AE }$ , etc. (ii) $\overleftrightarrow { AE }$, etc. (iii) $\overleftrightarrow { CO } \quad or\quad \overleftrightarrow { OC }$ (iv) $\overleftrightarrow { CO } ,\overleftrightarrow { AE } \quad ;\quad \overleftrightarrow { AE } ,\overleftrightarrow { EF }$

Question 7.
From the given figure, write

(i) collinear points
(ii) concurrent lines and their points of concurrence.

(i) A, D, C ; B, D, E.
(ii) l, n, p ; point B and m, p, q ; point A.

#### Question 8

In the given figure, write

(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines,
(iii) concurrent lines.
(iv) collinear points.

#### Question 10

(i) Name all the rays shown in the following figure whose initial points are A, B and C respectively.

(ii) Is ray AB different from ray AD?
(iii) Is ray CA different from ray CE?
(iv) Is ray BA different from ray CA?
(v) Is ray ED different from ray DE?

#### Question 11

Consider the following figure of line $\overleftrightarrow { MN }$. Says whether following statements are true or false in context of the given figure.

(i) Q, M, O, N and P are points on the line $\overleftrightarrow { MN }$.
(ii) M, O and N are points on a line segment $\overline{\mathrm{MN}}$.
(iii) M and N are end points of line segment $\overline{\mathrm{MN}}$ .
(iv) O and N are end points of line segment $\overline{\mathrm{OP}}$.
(v) M is a point on the ray $\overline{\mathrm{OP}}$.
(vi) M is one of the end points of line segment $\overline{\mathrm{QO}}$.
(vii) Ray $\overrightarrow { OP }$ is same as ray $\overrightarrow { OM }$.
(viii)Ray $\overrightarrow { OM }$ is not opposite to ray $\overrightarrow { OP }$.
(ix) Ray $\overrightarrow { OP }$ is different from ray $\overrightarrow { QP }$.
(x) O is not an initial point of ray $\overrightarrow { OP }$.
(xi) N is the initial point of $\overrightarrow { N }$ and $\overrightarrow { NM }$.

(i) True.
(ii) True.
(iii) True.
(iv) False.
(v) False.
(vi) False.
(vii) False.
(viii) False.
(ix) True.
(x) False.
(xi) True.

### Basic Geometrical Concept Class-6 ML Aggarwal ICSE Mathematics  Solutions Exercise- 10.2

#### Question 1

How many angles are shown in the following figure? Name them.

∠A, ∠B, ∠C, ∠D. Four angles.

#### Question 2.

In the given figure, name the point(s)
(i) In the interior of ∠DOE
(ii) In the exterior of ∠EOF
(iii) On ∠EOF

(i) A
(ii) C, A, D
(iii) E, B, O, F

#### Question 3

Draw rough diagrams of two angles such that they have
(i) One point in common.
(ii) Two points in common.
(iii) One ray in common.

(i)

∠AOB and ∠BOC have one point O in common.
(ii) ∠AOB and ∠OBC have two points O and B in common.

∠AOB and ∠BOC have one ray $\overrightarrow{\mathrm{OB}}$ in common.

### ML Aggarwal ICSE Mathematics Solutions Basic Geometrical Concept  Exercise- 10.3 for ICSE Class-6 Mathematics

#### Question 1

Draw rough diagrams to illustrate the following:
(i) open simple curve
(ii) closed simple curve
(iii) open curve that is not simple
(iv) closed curve that is not simple.

#### Question 2

Consider the given figure and answer the following questions:
(i) Is it a curve?
(ii) Is it a closed curve?
(iii) Is it a polygon?

(i) Yes, it is a curve.
(ii) Yes, it is a closed curve.
(iii) Yes, it is a polygon.

Question 3.
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?

The point A is neither in the exterior nor in the interior of triangle ABC. It is on the triangle ABC.

Question 4

Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them.

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

Question 5.
In context of the given figure:
(i) Is it a simple closed curve?
(iii) Draw its diagonals and name them.
(iv) State which diagonal lies in the interior and which diagonal lies in the exterior of the quadrilateral.

(i) Yes
(ii) Yes.
(iii) Its diagonals are $\overline{\mathrm{AC}}$ and $\overline{\mathrm{BD}}$.
(iv) Diagonal $\overline{\mathrm{AC}}$ is in the interior and diagonal $\overline{\mathrm{BD}}$ is in the exterior of quadrilateral ABCD.

#### Question 6

Draw a rough sketch of a quadrilateral KLMN. State,
(i) two pairs of opposite sides
(ii) two pairs of opposite angles
(iii) two pairs of adjacent sides
(iv) two pairs of adjacent angles.

### Exercise-10.4, ML Aggarwal ICSE Mathematics Solutions Basic Geometrical Concept

#### Question 1

In the given figure, identify:
(i) the centre of the circle
(iii) a diameter
(iv) a chord
(v) two points in the interior
(vi) a point in the exterior
(vii) a sector
(viii) a segment

(i) O is the centre of the circle.
(ii) $\overline{\mathrm{OA}}, \overline{\mathrm{OB}}, \overline{\mathrm{OC}}$ are three radii of the circle.
(iii) $\overline{\mathrm{AC}}$ is a diameter of the circle.
(iv) $\overline{\mathrm{ED}}$ is a chord of the circle.
(v) O and P are two points in the interior.
(vi) Q is a point in the exterior.
(vii) OAB (shaded portion) is a sector of the circle.
(viii)Shaded portion of the circular region enclosed by line segment ED and the corresponding arc.

Question 2.
State whether the following statements are true (T) or false (F):
(i) Every diameter of a circle is also a chord.
(ii) Every chord of a circle is also a diameter.
(iii) Two diameters of a circle will necessarily intersect.
(iv) The centre of the circle is always in its interior.

(i) True.
(ii) False.
(iii) True.
(iv) True.

### Objective Type Questions ML Aggarwal ICSE Mathematics Solutions Chapter-10 Basic Geometrical Concept  for ICSE Class-6 Mathematics

#### Question 1

Fill in the blanks:
(i) There is exactly one line passing through ……….. distinct points in a plane.
(ii) Two different lines in a plane either ……….. at exactly one point or are parallel.
(iii) The curves which have different beginning and end points are called ……….. curves.
(iv) A curve which does not cross itself at any point is called a ……….. curve.
(v) A simple closed curve made up entirely of line segments is called a ………..
(vi) A line segment formed by joining two non- adjacent vertices of a polygon is called its ………..
(vii) A quadrilateral has ……….. diagonals.
(viii) A lines segment has a ……….. length.

(i) There is exactly one line passing through two distinct points in a plane. .
(ii) Two different lines in a plane either intersect at exactly one point or are parallel.
(iii) The curves which have different beginning and end points are called open curves.
(iv) A curve which does not cross itself at any point is called a simple curve.
(v) A simple closed curve made up entirely of line segments is called a polygon.
(vi) A line segment formed by joining two non- adjacent vertices of a polygon is called its diagonal.
(vii) A quadrilateral has two diagonals.
(viii) A lines segment has a definite length.

Question 2.
Fill in the blanks with correct word(s) to make the statement true.
(i) Radius of a circle is one-half of its ………..
(ii) A radius of a circle is a line segment with one end point at ……….. and the other end-point on
(iii) A chord of a circle is a line segment with its end points ………..
(iv) A diameter of a circle is a chord that ……….. the centre of the circle.
(v) All radii of a circle are ………..

(i) Radius of a circle is one-half of its diameter.
(ii) A radius of a circle is a line segment with one end point at the centre and the other end-point on the circle.
(iii) A chord of a circle is a line segment with its end points on the circle.
(iv) A diameter of a circle is a chord that passes through the centre of the circle.
(v) All radii of a circle are equal.

#### Question 3

State whether the following statements are true (T) or false (F):
(i) The line segment AB is the shortest route from A to B.
(ii) A line cannot be drawn wholly on a sheet of paper..
(iii) A line segment is made of infinite (uncountable) number of points.
(iv) Two lines in a plane always intersect.
(v) Through a given point only one line can be drawn.
(vi) Two different lines can be drawn passing through two distinct points.
(vii) Every simple closed curve is a polygon.
(viii)Every polygon has atleast three sides.
(ix) A vertex of a quadrilateral lies in its interior.
(x) A line segment with its end-points lying on a circle is called a diameter of the circle.
(xi) Diameter is the longest chord of the circle.
(xii) The end-points of a diameter of a circle divide the circle into two points, each part is called a semi-circle.
(xiii) A diameter of a circle divides the circular region into two parts, each part is called a semi-circular region.
(xiv) The diameter’s of a circle are concurrent the centre of the circle is the point common to all diameters.
(xv) Every circle has unique centre and it lies inside the circle.
(xvi) Every circle has unique diameter.

(i) The line segment $\overline{\mathrm{AB}}$ is the shortest route from A to B. True
(ii) A line cannot be drawn wholly on a sheet of paper. True
(iii) A line segment is made of infinite (uncountable) number of points. True
(iv) Two lines in a plane always intersect. False
(v) Through a given point only one line can be drawn. False
(vi) Two different lines can eb drawn passing through two distinct points. False
(vii) Every simple closed curve is a polygon. False
(viii)Every polygon has atleast three sides. True
(ix) A vertex of a quadrilateral lies in its interior. False
(x) A line segment with its end-points lying on a circle is called a diameter of the circle. False
(xi) Diameter is the longest chord of the circle. True
(xii) The end-points of a diameter of a circle divide the circle into two points, each part is called a semi-circle. True
(xiii) A diameter of a circle divides the circular region into two parts, each part is called a semi-circular region. True
(xiv)The diameter’s of a circle are concurrent the centre of the circle is the point common to all diameters. True
(xv) Every circle has unique centre and it lies inside the circle. True
(xvi) Every circle has unique diameter. False

#### Choose the correct answer from the given four options (4 to 20):

Question 4.
Which of the following has no end points?
(a) a line
(b) a ray
(c) a line segment
(d) none of these

a line
Because it cannot be drawn on a paper, (a)

Question 5.
Which of the following has definite length?
(a) a line
(b) a ray
(c) a line segment
(d) none of these

a line segment
Because a line segment can be drawn on a paper and it has two end points. (c)

Question 6

The number of points required to name a line if
(a) 1
(b) 2
(c) 3
(d) 4

2
A line has no definite length but. It requires $\overrightarrow{\mathrm{AB}}$ to represent it. (b)

#### Question 7.

The number of lines that can be drawn through a given point is
(a) 1
(b) 2
(c) 3
(d) infinitely many

Infinitely many. (d)

#### Question 8.

The number of lines that can be drawn passing through two distinct points is
(a) 1
(b) 2
(c) 3
(d) inifinitely many

1 (a)

Question 9.
The maximum number of points of intersection of three lines drawn in a plane is
(a) 1
(b) 2
(c) 3
(d) 6

3 (c)

Question 10.
The minimum number of points of intersection of three lines drawn in a plane is
(a) 0
(b) 1
(c) 2
(d) 3

0 (a)

Question 11.
In the given figure, the number of line segment is
(a) 5
(b) 10
(c) 12
(d) 15

5 (c)

#### Question 12

In a polygon with 5 sides, the number of diagonals is
(a) 3
(b) 4
(c) 5
(d) 10

5 (c)

#### Question 13.

The number of lines passing through 5 points such that no three of them are collinear are
(a) 10
(b) 5
(c) 8
(d) 20

10 (a)

Question 14.
In context of the given figure, which of the following statement is correct ?
(a) B is not a point on segment $\overline{\mathrm{AC}}$
(b) B is the initial point of the ray $\overrightarrow{\mathrm{AD}}$
(c) D is a point on the ray $\overrightarrow{\mathrm{CA}}$
(d) C is a point on the ray $\overrightarrow{\mathrm{BD}}$

C is a point on the ray BD (d)

Question 15.
The figure formed by two rays with same initial point is known as
(a) a line
(b) a line segment
(c) a ray
(d) an angle

an angle (d)

Question 16.
In the given figure, the number of angles is
(a) 3
(b) 4
(c) 5
(d) 6

6 (d)

Question 17.
Which of the following statements is false?
(a) A triangle has three sides
(b) A triangle has three vertices
(c) A triangle has three angles
(d) A triangle has two diagonals

A triangle has two diagonals (d)

Question 18.
Which of the following statements is false?
(a) A quadrilateral has four sides and four vertices
(b) A quadrilateral has four angles
(c) A quadrilateral has four diagonals
(d) A quadrilateral has two diagonals

A quadrilateral has four diagonals (c)

Question 19.
By joining any two points of a circle, we obtain its
(b) chord
(c) diameter
(d) circumference

chord (b)

Question 20.
If the radius of a circle is 4 cm, then the length of its diameter is
(a) 2 cm
(b) 4 cm
(c) 8 cm
(d) 16 cm

8 cm (c)

#### Higher Order Thinking Skills ( HOTS ) Chapter-10 ICSE Class-6 Maths

Question 1.

Can a sector and segment of a circle coincide? If so, name it.

Yes, a semicircle.

#### Question 2.

In the given figure, find:
(i) the number of triangles pointing up.
(ii) the total number of triangles.

(i) The number of triangles pointing up are = 1 + 3 + 6 = 10
(ii) Total number of triangles = 13

#### Question 3

In the given figure, find the total number of squares.

Total number of squares in the given figure are
= 1 + 4 + 9 + 16 = 30

#### Question 1

(i) Name all the rays shown in the given figure whose initial point is A.
(ii) Is ray $\overrightarrow{\mathrm{AB}}$ different from ray $\overrightarrow{\mathrm{AD}}$ ?
(iii) Is ray $\overrightarrow{\mathrm{CA}}$ different from ray $\overrightarrow{\mathrm{CE}}$ ?
(iv) Is ray $\overrightarrow{\mathrm{BA}}$ different from ray $\overrightarrow{\mathrm{CA}}$ ?
(v) Is ray $\overrightarrow{\mathrm{ED}}$ different from ray $\overrightarrow{\mathrm{DE}}$ ?

(i) $\overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{AC}}, \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{AE}}$
(ii) No.
(iii) No.
(iv) Yes.
(v) Yes.

#### Question 2

From the given figure, write

(i) all pairs of parallel lines.
(ii) all pairs of intersecting lines.
(iii) lines whose point of intersecting is E.
(iv) collinear points.

(i) l, m
(ii) l, n; l, p; m, n; m, p; n, p
(iii) l, p
(iv) {A, B, C} and {A, E, D}

#### Question 3.

In the given figure :

(a) Name;
(i) Parallel lines.
(ii) All pairs of intersecting lines.
(iii) concurrent lines.
(b) State wheather true or false:
(i) points A, B and D are collinear.
(ii) lines AB and ED interesect at C.

(a) (i) AB, ED are parallel lines.
(ii) $\overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{AD}} ; \overrightarrow{\mathrm{AB}}, \overrightarrow{\mathrm{CD}} ; \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{ED}} ; \overrightarrow{\mathrm{ED}}$$\overrightarrow{\mathrm{CD}} ; \overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{CD}}$
(iii) $\overrightarrow{\mathrm{AD}}, \overrightarrow{\mathrm{ED}}, \overrightarrow{\mathrm{CD}}$.
(b)
(i) False.
(ii) False.

#### Question 4

In context of the given figure, state whether the following statements are true (T) or false (F):

(i) Point A is in the interior of ∠AOD.
(ii) Point B is in the interior of ∠AOC.
(iii) Point C is in the exterior of ∠AOB.
(iv) Point D is in the exterior of ∠AOC.

(i) False.
Correct: Poin A is exterior of ∠AOD.
(ii) True.
(iii) True.
(iv) True.

Question 5.
How many angles are marked in the given figure? Name them?

Five angles.
Names are : ∠QPR, ∠PRQ, ∠TQR, ∠PQT, ∠PQR.

#### Question 6.

In context of the given figure, name
(i) all triangles
(ii) all triangles having point E as common vertex.

(i) ∆ABC, ∆DBC, ∆EBC, ∆EAB, ∆DEC.
(ii) ∆EBC, ∆EAB, ∆DEC.

#### Question 7

In context of the given figure, answer the following questions:

(i) Is ABCDEFG a polygon?
(ii) How many sides does it have?
(iii) How many vertices does it have?
(iv) Are $\overline{\mathrm{AB}}$ and $\overline{\mathrm{FE}}$ adjacent sides?
(v) Is $\overline{\mathrm{GF}}$ a diagonal of the polygon?
(vi) Are $\overline{\mathrm{AC}}, \overline{\mathrm{AD}} \text { and } \overline{\mathrm{AE}}$ diagonals of the polygon?
(vii) Is point P in the interior of the polygon?
(viii)Is point A in the exterior of the polygon?

(i)Yes
(ii) Seven
(iii) Seven
(iv) No
(v) No
(vi) Yes
(vii) No
(viii) No

-: End of Basic Geometrical Concept Class-6 ML Aggarwal Solutions  :–