# 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. 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. 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