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

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.

## NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas Exercise: 4.1

Q1 Use the figure to name :

(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)

Q2 Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

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.

Q3 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.

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.

Q5 (a) Draw a rough figure and label suitably in each of the following cases: Point P lies on .

Answer: (a)

Q5 (b) Draw a rough figure and label suitably in each of the following cases: and intersect at M.

Answer: (b)

Q5 (c) Draw a rough figure and label suitably in each of the following cases: Line contains E and F but not D.

Answer: (c)

Q5 (d) Draw a rough figure and label suitably in each of the following cases: and meet at O.

Answer: (d)

Q6 Consider the following figure of line . 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 .

(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

## NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas Exercise: 4.2

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

Answer: (a) Open

(b) Closed

(c) Open

(d) Closed

(e) Closed

Q2 Draw rough diagrams to illustrate the following :

(a) Open curve (b) Closed curve.

Answer: (a)

(b)

Q3 Draw any polygon and shade it is interior.

Answer: Polygon ABCDEF

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.

## NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas Exercise: 4.3

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.

## NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas Exercise: 4.4

Q1 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?

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.

## NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas Exercise: 4.5

Q1 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?

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

## NCERT solutions for class 6 maths chapter 4 Basic Geometrical Ideas Exercise: 4.6

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.

Q3 Draw any circle and mark

(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.

Q4 Say true or false :

(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.

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#### Reference Books Solutions

- HC Verma Part 1
- HC Verma Part 2
- RD Sharma Class 9
- RD Sharma Class 10
- RS Aggarwal Class 10
- Lakhmir Singh Class 9
- Lakhmir Singh Class 10