## MP Board Class 6th Maths Solutions Chapter 4 Basic Geometrical Ideas Ex 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 : O, B, C, D, E

(b) A line \(\overleftrightarrow { DB }\)

(c) Four rays \(\overrightarrow{O D}\), \(\overrightarrow{O E}\), \(\overrightarrow{O C}\), \(\overrightarrow{O B}\)

(d) Five line segments :

\(\overline{D E}\), \(\overline{O E}\), \(\overline{O C }\), \(\overline{O B}\), \(\overline{O D}\).

Question 2.

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

Solution:

Possible lines are \(\overleftrightarrow { AB }\), \(\overleftrightarrow { AC }\), \(\overleftrightarrow { AD }\), \(\overleftrightarrow { BC }\), \(\overleftrightarrow { BD }\), \(\overleftrightarrow { CD }\), \(\overleftrightarrow { BA }\), \(\overleftrightarrow { CA }\), \(\overleftrightarrow { DA }\), \(\overleftrightarrow { CB }\), \(\overleftrightarrow { DB }\), \(\overleftrightarrow { DC }\).

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:

(a) A line containing point E is \(\overleftrightarrow { AE }\).

(b) A line passing through A is \(\overleftrightarrow { AE }\).

(c) A line on which O lies is \(\overleftrightarrow { CO }\) or \(\overleftrightarrow { OC }\).

(d) Two pairs of intersecting lines are \(\overleftrightarrow { AD }\), \(\overleftrightarrow { CO }\) and \(\overleftrightarrow { AE }\), \(\overleftrightarrow { FE }\).

Question 4.

How many lines can pass through

(a) one given point?

(b) two given points?

Solution:

(a) Infinite number of lines can pass through one given point.

(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 Plies on \(\overline{A B}\).

(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 \(\overleftrightarrow { MN }\). 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 \(\overline{M N}\).

(c) M and N are end points of line segment \(\overline{M N}\).

(d) O and N are end points of line segment \(\overline{O P}\).

(e) M is one of the end points of line segment \(\overline{Q O}\).

(f) M is point on ray \(\overrightarrow { OP }\)

(g) Ray \(\overrightarrow { OP }\) is different from ray \(\overrightarrow { OP }\).

(h) Ray 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:

(a) True

(b) True

(c) True

(d) False

(e) False

(f) False

(g) True

(h) False

(i) False

(j) False

(k) True