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

Written by Team Trustudies
Updated at 2021-05-07

## NCERT solutions for class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.1

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

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) Five points $$\rightarrow$$ B, C, O, E and D.
(b) A line $$\rightarrow$$ $$\overleftrightarrow$$BD
(c) Four rays $$\rightarrow$$ $$\overrightarrow {OC}, \overrightarrow {OB}, \overrightarrow {OD}, \overrightarrow {OE}$$
(d) Five line segments $$\rightarrrow$$ $$\overline {OD}, \overline {OE}, \overline {OC}, \overline {OB}, \overline {BC}$$

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

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

$$\overleftrightarrow {AB}$$ , $$\overleftrightarrow {AC}$$ $$\overleftrightarrow {AD}$$ ,$$\overleftrightarrow {BC}$$ , $$\overleftrightarrow {BD}$$ ,$$\overleftrightarrow {CD}$$ , $$\overleftrightarrow {BA}$$ ,$$\overleftrightarrow {CA}$$ , $$\overleftrightarrow {DA}$$ ,$$\overleftrightarrow {CB}$$ , $$\overleftrightarrow {DB}$$ ,$$\overleftrightarrow {DC}$$ ,

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.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) $$\overleftrightarrow {AE}$$
(b) $$\overleftrigharrow {AE}$$
(c) $$\overleftrigharrow {OC}$$
(d) $$\overleftrigharrow {AE} , \overleftrigharrow {OC} and \(\overleftrigharrow {AE}, \(\overleftrigharrow {EF} Q.4 How many lines can pass through (a) one given point? (b) two given points? NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : (a) infinite line passes through one given point. (b) only one line passes through two given points . Q.5 Draw a rough figure and label suitably in each of the following cases: (a) Point P lies on \(\overline {AB}$$ .
(b) $$\overleftrightarrow {XY}$$ and $$\overleftrightarrow {PQ}$$ intersect at M.
(c) Line L contains E and F but not D.
(d) $$\overleftrightarrow {OP}$$ and $$\overleftrightarrow {OQ}$$ meet at O.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(d)

Q.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 $$\overleftrightline {MN}$$ .
(b) M, O, N are points on a line segment $$\overline {MN}$$.
(c) M and N are end points of line segment $$\overtime {MN}$$.
(d) O and N are end points of line segment $$\overline {OP}$$ .
(e) M is one of the end points of line segment $$\overline {QO}$$.
(f) M is point on ray $$\overrightarrow {OP}$$.
(g) Ray$$\overleftrightarrow {OP}$$ is different from ray $$\overrightarrow {QP}$$.
(h) Ray $$\overleftrightarrow {OP}$$ is same as ray $$\overrightarrow {OM}$$ .
(i) Ray $$\overrightarrow {OM} is not opposite to ray \(\overleftrightarrow {OP}$$.
(j) O is not an initial point of $$\overleftrightarrow {OP}$$.
(k) N is the initial point of $$\overrightarrow {NP}$$ and $$\overrightarrow {NM} NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas 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 1. Classify the following curves as (i) Open or (ii) Closed NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : (a) open curve (b) closed curve (c) open curve (d) closed curve (e) closed curve Q.2. Draw rough diagrams to illustrate the following: (a) Open curve (b) Closed curve NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : Q.3 Draw any polygon and shade its interior. NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : Q.4 Consider the given figure and answer the questions: (a) Is it a curve? (b) Is it closed? NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : (a) Yes, it is a curve. (b) Yes, it is closed curve. Q.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. NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : (b) No its not possible ## NCERT solutions for class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.3 Q.1 Name the angles in the given figure. NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Answer : The angles are: (i) \(\angle A or \angle DAB$$
(ii) $$\angle B or \angle CBA$$
(iii) $$\angle C or \angle DCB$$
(iv) $$\angle D or \(\angle ADC.$$

Q.2 In the given diagram, name the points(s)
(a) In the interior of ?DOE
(b) In the exterior of ?EOF
(c) On ?EOF

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) A
(b) C is in the exterior of $$\angle$$EOF.
(c) B is on the $$\angle$$EOF.

Q.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.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

## NCERT solutions for class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.4

Q.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?

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

Q.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 $$\angle$$B as common?

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) The three triangles are $$\triangle$$ABD, $$\triangle$$ ABC, $$\triangle$$ADC
(b) The angles are $$\angle BAC, \angle BAD, \angle CAD,$$
$$\angle ADB, \angle ADC, \angle ABC, \angle ACB$$
(c) The line segments are AB, BC, CA , AD, BD and DC
(d) $$\angle$$ABD and $$\angle$$ABC are triangles which have $$\angle$$B as common.

## NCERT solutions for class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.5

Q.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?

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

PR and QS are the diagonals. They meet at point O which is in the interior of the quadrilateral.

Q.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.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) Two pairs of opposite sides are KL, NM and KN , LM
(b) Two pairs of opposite angles are $$\angle$$KLM, $$\angle$$KNM and $$\angle$$LKN, $$\angle$$LMN
(c) Two pairs of adjacent sides are KL, LM and KN, NM
(d) (d) Two pairs of adjacent angles are $$\angle$$K, $$\angle$$L and $$\angle$$M, $$\angle$$N or $$\angle$$K, $$\angle$$L and $$\angle$$L, $$\angle$$M

## NCERT solutions for class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.6

Q.3 Draw any circle and mark
(a) its centre
(c) a diameter
(d) a sector
(e) a segment
(f) a point in its interior
(g) a point in its exterior
(h) an arc

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) The centre of the circle is O.
(c) A diameter is AB
(d) A sector is AOC
(e) A segment is PQ
(f) A point in its interior is F
(g) A point in its exterior is E
(h) An arc is PQ

Q.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.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) True
(b) True

Q.1 From the figure, identify:
(a) the centre of circle
(c) a diameter
(d) a chord
(e) two points in the interior
(f) a point in the exterior
(g) a sector
(h) a segment

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

(a) The centre of circle is O
(b) Three radii are OA, OB, 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) A sector is AOB i.e shaded region
(h) A segment is ED i.e shaded region

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

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas