Class 6 Maths NCERT Solutions for Chapter 4 Basic Geometrical Ideas Ex - 4.1

Basic Geometrical Ideas

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 $\overleftrightarrow { OC } ,\overleftrightarrow { OB } ,\overleftrightarrow { OD }$ and $\overleftrightarrow { ED }$ .
(d) 5 line segments are $\overline { OE } ,\overline { OD } ,\overline { DE, } \overline { OB }$ and $\overline { BD }$ .

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

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.
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas 3
Solution:
Clearly, from the given figure
(a) Line containing pqint E is $\overleftrightarrow { AE }$ .
(b) Line passing through A is $\overleftrightarrow { AE }$ .
(c) O lies on the line $\overleftrightarrow { CB }$ .
(d) Two pairs of intersecting lines are $\overleftrightarrow { CO } ,\overleftrightarrow { AE }$ and $\overleftrightarrow { AE } ,\overleftrightarrow { EF }$ .

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.

Question 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.

Solution:
A rough figure and labelled suitably for the given cases are as under:
(a) Point P lies on $\overleftrightarrow { AB }$ :

(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 7

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 $\overleftrightarrow { MN }$ .
(b) M, O, N are points on a line segment $\overline { MN }$ .
(c) M and N are end points of line segment $\overline { MN }$ .
(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 $\overrightarrow { OP }$ is different from ray $\overrightarrow { QP }$ .
(h) Ray $\overrightarrow { OP }$ is same as ray $\overrightarrow { OM }$ .
(i) Ray $\overrightarrow { OM }$ is not opposite to ray $\overrightarrow { OP }$ .
(j) O is not an initial point of $\overrightarrow { OP }$ .
(k) N is the initial point of $\overrightarrow { NP }$ and $\overrightarrow { NM }$ .

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

Basic Geometrical Ideas

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Class 6 Maths NCERT Solutions for Chapter 4 Basic Geometrical Ideas Ex – 4.1

Basic Geometrical Ideas

Class 6 Maths NCERT Solutions for Chapter 3 Playing with Numbers Ex 3.7

Class 6 Maths NCERT Solutions for Chapter 4 Basic Geometrical Ideas Ex – 4.2

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