NCERT Solutions for Class 6 Maths: One of the most important and interesting things to keep in mind is that these solutions available are totally free of cost. This also includes all the solutions to the exercises that are given in the textbook. NCERT solutions for class 6 maths gives you chapter-wise solutions to each and every question. This can help you solve even the tougher with ease.
It is always good to have a strong foundation in order to build a good building. This also is true in class when you are still learning the basics of maths. NCERT solutions for class 6 maths provides you the exact opportunity to build a strong foundation in this subject. Below is an overview of each and every chapter covered in the NCERT textbook.
Table of Contents
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas
Ex 4.1 Class 6 Maths Question 1.
Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Solution:
Clearly, from the given figure
(a) 5 points are points, O, C, B, D and E.
(b) A line is [altex]\overleftrightarrow { BD } [/latex]
(c) 4 rays are OC←→,OB←→,OD←→ and ED←→.
(d) 5 line segments are OE¯¯¯¯¯¯¯¯,OD¯¯¯¯¯¯¯¯,DE,¯¯¯¯¯¯¯¯¯OB¯¯¯¯¯¯¯¯ and BD¯¯¯¯¯¯¯¯.
Ex 4.1 Class 6 Maths Question 2.
Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
Solution:
All the possible ways of naming the given by choosing only two letters at a time out of 4 letters are
AB←→,AC←→,AD←→,BC←→,BD←→,CD←→,DC←→,DB←→,CB←→,DA←→,CA←→ and BA←→.
Ex 4.1 Class 6 Maths Question 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.
Solution:
Clearly, from the given figure
(a) Line containing pqint E is AE←→.
(b) Line passing through A is AE←→.
(c) O lies on the line CB←→.
(d) Two pairs of intersecting lines are CO←→,AE←→ and AE←→,EF←→.
Ex 4.1 Class 6 Maths Question 4.
How many lines can pass through
(a) one given point?
(b) two given points?
Solution:
(a) An unlimited number of lines can be drawn passing through a given point.
(b) Exactly one line can be drawn passing through two different given points in a plane.
Ex 4.1 Class 6 Maths Question 5.
Draw a rough figure and label suitably in each of the following cases:
(a) Point P lies on AB¯¯¯¯¯¯¯¯.
(b) XY←→ and PQ←→ intersect at M.
(c) Line l contains E and F but not D.
(d) OP←→ and OQ←→ meet at O.
Solution:
A rough figure and labelled suitably for the given cases are as under:
(a) Point P lies on AB←→ :
(b) XY←→ and PQ←→ intersect at M:
(c) Line l contains E and F but not D:
(d) OP←→ and OQ←→ meet at O.
Ex 4.1 Class 6 Maths Question 6.
Consider the following figure of line MN. 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 MN←→− .
(b) M, O, N are points on a line segment MN¯¯¯¯¯¯¯¯¯¯.
(c) M and N are end points of line segment MN¯¯¯¯¯¯¯¯¯¯.
(d) O and N are end points of line segment OP¯¯¯¯¯¯¯¯.
(e) M is one of the end points of line segment QO¯¯¯¯¯¯¯¯.
(f) M is point on ray OP−→−.
(g) Ray OP−→− is different from ray QP−→−.
(h) Ray OP−→− is same as ray OM−→−.
(i) Ray OM−→− is not opposite to ray OP−→−.
(j) O is not an initial point of OP−→−.
(k) N is the initial point of NP−→− and NM−→−.
Solution:
In the context of the given figure, the given statement is:
(a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) True
(j) False
(k) True
Ex 4.2 Class 6 Maths Question 1.
Classify the following curves as
(i) Open or
(ii) Closed.
Solution:
Open curves are (a) and (c) and closed curves are (b), (d) and (e).
Ex 4.2 Class 6 Maths Question 2.
Draw rough diagrams to illustrate the following:
(a) Open curve
(b) Closed curve
Solution:
Rough diagram to illustrate
(a) Open curve is
(b) Closed curve is
Ex 4.2 Class 6 Maths Question 3.
Draw any polygon and shade its interior.
Solution:
We know that in a closed curve, the interior is inside of the curve. Thus, shaded portion of the polygon indicate its interior.
Ex 4.2 Class 6 Maths Question 4.
Consider the given figure and answer the questions:
(a) Is it a curve?
(b) Is it closed?
Solution:
(a) Yes, the given figure represents a curve.
(b) Yes, the curve is closed.
Ex 4.2 Class 6 Maths Question 5.
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.
Solution:
(a) Impossible, as a close plane figure bounded by lines is called a polygon.
(b) Yes, it may be as
(c) No, impossible, as a polygon of two sides cannot be drawn.
Ex 4.3 Class 6 Maths Question 1.
Name the angles in the given figure.
Solution:
The angles in the given figure are named as ∠ABC, ∠BCD, ∠CDA and ∠DAB.
Ex 4.3 Class 6 Maths Question 2.
In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF
Solution:
Clearly, from the given figure :
(a) The point A lies in the interior of ∠DOE. .
(b) The points A and C lie in the exterior of ∠EOF.
(c) The points E, B, O and F lie on ∠EOF.
Ex 4.3 Class 6 Maths Question 3.
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
Solution:
(a) The diagram is shown as below
Here, ∠ROQ and ∠QOP have one point O in common.
(b) The diagram is shown as below
Here, ∠MON and ∠ONR have two points O and N in common.
(c) Drawing a diagram of two angles, such that they have three points in common, is not possible.
(d) Drawing a diagram of two angles, such that they have four points in common, is not possible.
(e) In the figure given below, ∠SOT and ∠POT have one ray OT−→− in common.
Ex 4.4 Class 6 Maths Question 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?
Solution:
Rough sketch of a ∠ABC as shown.
Points P and Q are marked in the interior and exterior of ∆ABC.
Point A lies on the ∆ABC.
Ex 4.4 Class 6 Maths Question 2.
(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 ZB as common?
Solution:
(a) Three triangles are identified in the figure as ∆ ABC, ∆ ABD and ∆ ACD.
(b) The names of seven angles are ∠BAD, ∠BAC, ∠CAD, ∠ABD, ∠ACD, ∠ADC and ∠ADB.
(c) The names of six line segments are AB, BD, DC, CA, BC and AD.
(d) ∆ ABC and ∆ ABD have ∠B as common.
Ex 4.5 Class 6 Maths Question 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?
Solution:
PQRS is a quadrilateral having PR and QS as its diagonals intersecting at the point O, which is in the interior of the quadrilateral PQRS.
Ex 4.5 Class 6 Maths Question 2.
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.
Solution:
KLMN is a quadrilateral.
(a) KL, MN and LM, KN are two pairs of its opposite sides.
(b) ∠K, ∠M and∠L, ∠N are two pairs of opposite angles.
(c) KL, LM and KN, NM are two pairs of adjacent sides.
(d) ∠K, ∠N and ∠L, ∠M are two pairs of adjacent angles.
Ex 4.5 Class 6 Maths Question 3.
Investigate:
Use strips and fasteners to make a triangle and a quadrilateral.
Try to push inward at any one vertex of the triangle. Do the same to the quadrilateral.
Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid?
Why is it that structures like electric towers make use of triangular shapes and not quadrilaterals?
Solution:
On pushing inward at any one vertex of the triangle, we find that the triangle is not distorted. Whereas doing so with the quadrilateral we find that it is distorted. Triangle is rigid. Thus, we make use of triangular shapes in structures like electric towers as triangular shapes are more rigid.
Ex 4.6 Class 6 Maths Question 1.
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
Solution:
(a) O is the centre of the circle.
(b) OA, OB and OC are three radii of circle.
(c) AC is a diameter of circle.
(d) ED is a chord of circle.
(e) Points O and P are in the interior of circle.
(f) Point Q is in the exterior of circle.
(g) OAB is a sector of circle.
(h) Shaded region in the interior of a circle enclosed by a chord ED.
Ex 4.6 Class 6 Maths Question 2.
(a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?
Solution:
(a) Yes, a diameter is the longest chord.
(b) Not always.
Ex 4.6 Class 6 Maths Question 3.
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
Solution:
Draw any circle and its various parts are as under :
(a) Its centre is O.
(b) Its radii are OA, OB and OC.
(c) Its diameter is AOC.
(d) Its sector is OAB.
(e) Shaded region in the interior of a circle enclosed by a chord PQ.
(f) M is a point in its interior.
(g) N is a point in its exterior.
(h) BC is an arc.
Ex 4.6 Class 6 Maths Question 4.
Say true or false:
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.
Solution:
(a) True, because each diameter passes through the centre of a circle.
(b) True.
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