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

Download NCERT solutions for class 6 Maths chapter 4: Basic Geometrical Ideas. Get appropriate solutions for all exercises of chapter 4.

Jul 11, 2019 12:23 IST
NCERT Solutions for Class 6 Maths Chapter 4 - Basic Geometrical Ideas

Get free NCERT solutions for class 6 Maths chapter 4:Basic Geometrical Ideas. Here you will find the latest updated solutions to prepare for the current academic session 2019-2020.Our experts have prepared easy and accurate solutions for all exercises given in class 6 Maths NCERT chapter 4. Students may read and download the solutions to refer the same whenever required.

Exercise 4.1

1. Use the figure to name:

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

Solution.

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

(b) Name of a line:  

(c) Four rays:

(d) Five line segments are:

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

Solution.

All the possible names for the given line can be written as follows:

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.

4. How many lines can pass through

(a) one given point?

(b) two given points?

Solution.

(a) Infinite number of lines can pass through a given point.

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

5. Draw a rough figure and label suitably in each of the following cases:

Solution.

6. Consider the following figure of line MN. Say whether following statements are true or false in context of the given figure.

Solution.

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True

Exercise 4.2

1. Classify the following curves as (i) open or (ii) closed.

Solution.

(a) Open

(b) Closed

(c) Open

(d) Closed

(e) Closed

2. Draw rough diagrams to illustrate the following:

(a) Open curve

(b) Closed curve

Solution.

3. Draw any polygon and shade its interior.

Solution.

4. Consider the given figure and answer the questions.


(a) Is it a curve?

(b) Is it closed?

Solution.

(a) Yes, it is a curve.

(b) Yes, it is closed.

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) Circle is a closed curve but not a polygon.

(b) Below is given an open curve made up entirely of line segments:

(c) It is not possible to have a polygon with two sides.

Exercise 4.3

1.Name the angles in the given figure.


Solution.

Angles given in figure are:

∠DAB,∠ABC,∠BCD,∠CDA

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.

(a) A is the point lying in the interior ∠DOE.

(b) C is the point lying in the exterior ∠EOF.

(c) B is the point lying on ∠EOF.

3.Draw rough diagrams of two angles such that they have

(а) 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) In the following figure, O is the common point of ∠AOC and ∠BOD.

(b) In the following figure, O and Bare the common points in ∠AOB and ∠BOC.

(c) In the following figure, O, D and B are the common points in ∠AOB and ∠BOC.

(d) In the following figure, O, D, E and B are the common points in ∠AOB and ∠BOC.

(e)  In the following figure, ray OB is common in both∠AOB and ∠DOB.

Exercise 4.4

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.

Required triangle ABC is the given below:

Point A is neither in the exterior nor in the interior. It lies on the triangle ABC.

2.(a) Identify three triangles in the figure.

(6) Write the names of seven angles.

(c) Write the names of six line segments.

(d) Which two triangles have B as common?

Solution.

(a) Three triangles are:

∆ABC, ∆ABD and ∆ADC.

(b) Names of seven angles are:

∠ABC,∠ADB,∠BAD,∠ADC, ∠ACD,∠DAC,∠BAC

(c) Names of six line segments are:

(c) ∆ABC and ∆ABD have ∠B as common.

Exercise 4.5

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.

Required quadrilateral PQRS is drawn as below:

Here PR and QS are its two diagonals.

The meeting point of the diagonals is O which lies in the interior of the quadrilateral

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.

Required quadrilateral KLMN is drawn as below:

 

(a)  Two pairs of opposite sides are:

(KL, MN) and (NK, ML)

(b)Two pairs of opposite angles are:

∠LKN and ∠LMN, ∠KLM and ∠KNM

(c) Two pairs of adjacent sides are:

KL and KN, NM and ML

(d) Two pairs of adjacent angles are:

∠LKN and ∠KLM, ∠LMN, and ∠KNM

Exercise 4.6

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) Centre of the circle is O.

(b) Three radii of the given circle are: OA, OB and OC.

(c)  Diameter of the circle is AC.

(d)  Chord of the circle is ED.

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

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

(g) Sector of the circle is AOB (shaded region).

(h) Segment of the circle is ED (shaded region).

2.(a) Is every diameter of a circle also a chord?

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

Solution.

(a) Yes, every diameter of a circle is its longest chord.

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

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.

Required circler can be drawn as follows:

In this circle,

(a) O is the center.

(b) OA is a radius.

(c)  AB is a diameter.

(d) OBC is a sector (shaded region)

(e) ED in the segment(shaded region)

(f) P is in the interior of the circle.

(g) Q is in the exterior of the circle.

(h)  BC is an arc of the circle.

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; Two diameters of a circle always intersect at the centre of that circle.

(b) True

Check chapter-wise NCERT Solutions for Class 6 Maths from the links given below:

NCERT Solutions for Class 6 Maths Chapter 1 - Knowing Our Numbers

NCERT Solutions for Class 6 Maths Chapter 2 - Whole Numbers

NCERT Solutions for Class 6 Maths Chapter 3 –Playing with Numbers

NCERT solutions for other chapters will be provided here very soon. Check here for the detailed and appropriate solutions.