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