Well-designed AP 6th Class Maths Textbook Solutions Chapter 4 Basic Geometrical Ideas Exercise 4.1 offers step-by-step explanations to help students understand problem-solving strategies.
Basic Geometrical Ideas Class 6 Exercise 4.1 Solutions – 6th Class Maths 4.1 Exercise Solutions
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, D and E.
b) Name of the line is \(\overleftrightarrow{\mathrm{BD}}\)
c) Four rays are: \( \overrightarrow{\mathrm{OC}}\), \( \overrightarrow{\mathrm{OB}}\), \( \overrightarrow{\mathrm{OE}}\) and \( \overrightarrow{\mathrm{OD}}\).
d) Five line segments are: \(\overline{\mathrm{OB}})\), \(\overline{\mathrm{OC}})\), \(\overline{\mathrm{BD}})\), \(\overline{\mathrm{BE}})\) and \(\overline{\mathrm{DE}})\)
Question 2.
Name the line given in all possible (twelve) ways, choosing only two letters at a time 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 O lies
d) Two pairs of intersecting lines.
Solution:
a) \(\overleftrightarrow{E F}\)
b) \(\overleftrightarrow{AE}\)
c) \( \overrightarrow{\mathrm{BC}}\) (or) \( \overrightarrow{\mathrm{EF}}\)
d) (i) \(\overleftrightarrow{CO}\) and \(\overleftrightarrow{AE}\)
(ii) \(\overleftrightarrow{AE}\) and \(\overleftrightarrow{E F}\)
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 a points.
Question 5.
Draw a rough figure and label suitably in each of the following cases:
a) Point P lies on \(\overline{\mathrm{AB}})\)
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.
Solution:
Question 6.
Consider the following figure of line \(\overleftrightarrow{\mathrm{MN}}\). 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 \(\overleftrightarrow{\mathrm{MN}}\).
b) M, O, N are points on a line segment \(\overline{\mathrm{MN}})\).
c) M and N are end points of line segment \(\overline{\mathrm{MN}})\).
d) O and N are end points of line segment \(\overline{\mathrm{OP}})\).
e) M is one of the end points of line segment \(\overline{\mathrm{QO}})\).
f) M is point on ray \(\overline{\mathrm{OP}})\).
g) Ray \( \overrightarrow{\mathrm{OP}}\) is different from ray \( \overrightarrow{\mathrm{QP}}\).
h) Ray \( \overrightarrow{\mathrm{OP}}\) is same as ray \( \overrightarrow{\mathrm{OM}}\).
i) Ray \( \overrightarrow{\mathrm{OM}}\) is not opposite to ray \( \overrightarrow{\mathrm{OP}}\).
j) O is not an initial point of \( \overrightarrow{\mathrm{OP}}\).
k) N is the initial point of \( \overrightarrow{\mathrm{NP}}\) and \( \overrightarrow{\mathrm{NM}}\).
Solution:
a) True
b) True
c) True
d) False
e) False
f) False
g) True
h) False
i) False
j) False
k) True