These NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Ex 4.1 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.1
Question 1.
Use the figure to name:
(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Answer:
(a) Five points are: O, B, C, D, E
(b) Aline: \([latex]\overleftrightarrow{\mathrm{DB}}\)[/latex]
(c) Four rays: \(\overrightarrow{\mathrm{OD}}, \overrightarrow{\mathrm{OE}}, \overrightarrow{\mathrm{OC}}, \overrightarrow{\mathrm{OB}}\)
(d) Four line segments: \(\overline{\mathrm{DE}}, \overline{\mathrm{OE}}, \overline{\mathrm{OC}}, \overline{\mathrm{OB}}, \overline{\mathrm{OD}}\)
Question 2.
Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
Answer:
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.
Answer:
(a) A line containing E = \(\overleftrightarrow{\mathrm{AE}}\) or \(\overleftrightarrow{\mathrm{EF}}\)
(b) A line passing through
A = \(\overleftrightarrow{\mathrm{AE}}\) or \(\overleftrightarrow{\mathrm{DE}}\)
(c) A line on which O lies = \(\overleftrightarrow{\mathrm{CO}}\) or \(\overleftrightarrow{\mathrm{OC}}\)
(d) Two pairs of intersecting lines are \(\overleftrightarrow{\mathrm{AE}}\) . \(\overleftrightarrow{\mathrm{CO}}\), and \(\overleftrightarrow{\mathrm{FE}}\)
Question 4.
How many lines can pass through
(a) one given point?
(b) two given points?
Answer:
(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 P lies on \(\overline{\mathbf{A B}}\).
(b) \(\overleftrightarrow{\mathrm{XY}}\) and \(\overleftrightarrow{\mathrm{PQ}}\) intersect at M.
(c) Line l contains E and F but not D.
(d) \(\overleftrightarrow{\mathrm{OP}}\) and \(\overleftrightarrow{\mathrm{OQ}}\) meet at O.
Answer:
Question 6.
Consider the following figure of line \(\begin{equation}
\overline{\mathrm{MN}}
\end{equation}\). 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 \(\begin{equation}
\overline{\mathrm{MN}}
\end{equation}\).
(b) M, O, N are points on a line segment \(\begin{equation}
\overline{\mathrm{MN}}
\end{equation}\).
(c) M and N are end points of line segment \(\begin{equation}
\overline{\mathrm{MN}}
\end{equation}\).
(d) O and N are end points of line segment \(\begin{equation}
\overline{\mathrm{OP}}
\end{equation}\).
(e) M is one of the end points of line segment \(\begin{equation}
\overline{\mathrm{QO}}
\end{equation}\).
(f) M is point on ray \(\begin{equation}
\overrightarrow{\mathrm{OP}}
\end{equation}\)
(g) Ray \(\begin{equation}
\overrightarrow{\mathrm{OP}}
\end{equation}\) is different from ray \(\begin{equation}
\overrightarrow{\mathrm{OP}}
\end{equation}\)
(h) Ray \(\begin{equation}
\overrightarrow{\mathrm{OP}}
\end{equation}\) is same as ray \(\begin{equation}
\overrightarrow{\mathrm{OM}}
\end{equation}\)
(i) Ray \(\begin{equation}
\overrightarrow{\mathrm{OM}}
\end{equation}\) not opposite to ray \(\begin{equation}
\overrightarrow{\mathrm{OP}}
\end{equation}\)
(j) O is not an initial point of \(\begin{equation}
\overrightarrow{\mathrm{OP}}
\end{equation}\)
(k) N is the initial point of \(\begin{equation}
\overrightarrow{\mathrm{NP}}
\end{equation}\) and \(\begin{equation}
\overrightarrow{\mathrm{NM}}
\end{equation}\).
Answer:
(a) True
(b) True
(c) True
(d) False
(e) False
(f) False
(g) True
(h) False
(j) False
(j) False
(k) True