Basic Geometrical Ideas-Solutions Ex-4.1

CBSE Class –VI Mathematics
NCERT Solutions
Chapter 4 Basic Geometrical Ideas (Ex. 4.1)

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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) A line: DE¯¯¯¯¯¯¯,$\overline{\text{DE}},$DB¯¯¯¯¯¯¯,$\overline{\text{DB}},$OE¯¯¯¯¯¯¯,$\overline{\text{OE}},$OB¯¯¯¯¯¯¯$\overline{\text{OB}}$

(c) Four rays: OD−→−,$\overrightarrow{\text{OD}},$OE−→−,$\overrightarrow{\text{OE}},$OC−→−,$\overrightarrow{\text{OC}},$OB−→−$\overrightarrow{\text{OB}}$

(d) Four line segments: DE¯¯¯¯¯¯¯,$\overline{\text{DE}},$OE¯¯¯¯¯¯¯,$\overline{\text{OE}},$OC¯¯¯¯¯¯¯¯,$\overline{\text{OC}},$OB¯¯¯¯¯¯¯,$\overline{\text{OB}},$, OD¯¯¯¯¯¯¯¯$\overline{\text{OD}}$

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

Answer: AB¯¯¯¯¯¯¯,$\overline{\text{AB}},$AC¯¯¯¯¯¯¯,$\overline{\text{AC}},$AD¯¯¯¯¯¯¯¯,$\overline{\text{AD}},$BC¯¯¯¯¯¯¯,$\overline{\text{BC}},$BD¯¯¯¯¯¯¯,$\overline{\text{BD}},$CD¯¯¯¯¯¯¯,$\overline{\text{CD}},$BA¯¯¯¯¯¯¯,$\overline{\text{BA}},$CA¯¯¯¯¯¯¯,$\overline{\text{CA}},$DA¯¯¯¯¯¯¯¯,$\overline{\text{DA}},$CB¯¯¯¯¯¯¯,$\overline{\text{CB}},$DB¯¯¯¯¯¯¯,$\overline{\text{DB}},$DC¯¯¯¯¯¯¯$\overline{\text{DC}}$

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.

Answer: (a) A line containing E = AE¯¯¯¯¯¯¯$\overline{\text{AE}}$ or FE¯¯¯¯¯¯¯$\overline{\text{FE}}$

(b) A line passing through A = AE¯¯¯¯¯¯¯$\overline{\text{AE}}$ or DE¯¯¯¯¯¯¯$\overline{\text{DE}}$

(c) A line on which O lies = CO¯¯¯¯¯¯¯¯$\overline{\text{CO}}$ or OC¯¯¯¯¯¯¯¯$\overline{\text{OC}}$

(d) Two pairs of intersecting lines are : AD¯¯¯¯¯¯¯¯,$\overline{\text{AD}},$CO¯¯¯¯¯¯¯¯$\overline{\text{CO}}$ and AE¯¯¯¯¯¯¯$\overline{\text{AE}}$, FE¯¯¯¯¯¯¯$\overline{\text{FE}}$

Question 4. How many lines can pass though:

(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 AB¯¯¯¯¯¯¯.$\overline{\text{AB}}.$

(b) XY¯¯¯¯¯¯¯¯$\overline{\text{XY}}$ and PQ¯¯¯¯¯¯¯$\overline{\text{PQ}}$ intersect at M.

(c) Line l$l$ contains E and F but not D.

(d) OP¯¯¯¯¯¯¯$\overline{\text{OP}}$ and OQ¯¯¯¯¯¯¯¯$\overline{\text{OQ}}$ meet at O.

Answer:

Question 6. Consider the following figure of line MN¯¯¯¯¯¯¯¯$\overline{\text{MN}}$. Say whether following statements are true or false in the context of the given figure:

(a) Q, M, O, N, P are points on the line MN¯¯¯¯¯¯¯¯$\overline{\text{MN}}$.

(b) M, O, N are points on a line segment MN¯¯¯¯¯¯¯¯$\overline{\text{MN}}$.

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

(d) O and N are end points of line segment OP¯¯¯¯¯¯¯$\overline{\text{OP}}$.

(e) M is one of the end points of line segment QO¯¯¯¯¯¯¯¯$\overline{\text{QO}}$.

(f) M is point on ray OP−→−$\overrightarrow{\text{OP}}$.

(g) Ray OP−→−$\overrightarrow{\text{OP}}$ is different from ray OP−→−$\overrightarrow{\text{OP}}$.

(h) Ray OP−→−$\overrightarrow{\text{OP}}$same as ray OM−→−.$\overrightarrow{\text{OM}}.$.

(i) Ray OM−→−.$\overrightarrow{\text{OM}}.$ is not opposite to ray OP−→−$\overrightarrow{\text{OP}}$.

(j) O is not an initial point of NP¯¯¯¯¯¯¯$\overline{\text{NP}}$ and NM¯¯¯¯¯¯¯¯$\overline{\text{NM}}$.

Answer: (a) True, (b) True, (c) True, (d) False, (e) False, (f) False, (g) True, (h) False, (i) False, (j) False, (k) True