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.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas 2
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

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