### Basic Geometrical Ideas - Solutions

CBSE Class –VI Mathematics

NCERT Solutions
Chaper 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

Answer:  (a) Five points are: O, B, C, D, E

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

(c) Four rays: $\stackrel{\to }{\text{OD}},$$\stackrel{\to }{\text{OE}},$$\stackrel{\to }{\text{OC}},$$\stackrel{\to }{\text{OB}}$

(d) Four line segments: $\overline{\text{DE}},$$\overline{\text{OE}},$$\overline{\text{OC}},$$\overline{\text{OB}},$$\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: $\overline{\text{AB}},$$\overline{\text{AC}},$$\overline{\text{AD}},$$\overline{\text{BC}},$$\overline{\text{BD}},$$\overline{\text{CD}},$$\overline{\text{BA}},$$\overline{\text{CA}},$$\overline{\text{DA}},$$\overline{\text{CB}},$$\overline{\text{DB}},$$\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 = $\overline{\text{AE}}$ or $\overline{\text{FE}}$

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

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

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

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

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

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

Question 6. Consider the following figure of line $\overline{\text{MN}}$. 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 $\overline{\text{MN}}$.

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

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

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

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

(f) M is point on ray $\stackrel{\to }{\text{OP}}$.

(g) Ray $\stackrel{\to }{\text{OP}}$ is different from ray $\stackrel{\to }{\text{OP}}$.

(h) Ray $\stackrel{\to }{\text{OP}}$same as ray $\stackrel{\to }{\text{OM}}.$.

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

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

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