NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas

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

Exercise 4.1

Question 1.
Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Solution:
(a) Five points are: O, B, C, E and D

(b) Name of the line is $\overleftrightarrow { DB }$ or $\overleftrightarrow { BD }$ .
(c) Four rays are: $\overrightarrow { OC }$ , $\overrightarrow { OB }$ , $\overrightarrow { OE }$ and $\overrightarrow { OD }$
(d) Five line segments are:
$\overline { OE }$ , $\overline { ED }$ , $\overline { OD }$ , $\overline { OB }$ and $\overline { EB }$ .

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

Solution:
The given lines can be named as follows:

Question 3.
Use the figure to name:
(a) Line containing point E.
(b) Line passing through A.
(c) Line on which 0 lies.
(d) Two pairs of intersecting lines.

Solution:
(a) $\overleftrightarrow { EF }$
(b) $\overleftrightarrow { AE }$
(c) $\overleftrightarrow { BC }$ or $\overleftrightarrow { BO }$
(d) $\overleftrightarrow { CO }$ or $\overleftrightarrow { AE }$ or $\overleftrightarrow { AE }$ or $\overleftrightarrow { EF }$

Question 4.
How many lines can pass through
(a) one given point?
(b) two given points?
Solution:
(a) Infinitely many lines can pass through a given points.
(b) Only one line can pass through two given points.

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:

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 $\overleftrightarrow { OP }$ 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 $\overrightarrow { NM }$ .
Solution:
(a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(i) False
(j) False
(k) True