### Chapter - 4 Basic Geometrical Ideas

Q
##### Basic Geometrical Ideas

Question:

1. Use the figure to name :

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

Solution: (a) The five points are O, B, C, D, and E.

(b) A line is $\underset{BD}{\leftrightarrow}$.

(c) The four rays are $\underset{OD,}{\rightarrow}\ \underset{OB,}{\rightarrow} \ \underset{OC,}{\rightarrow} \ \underset{OE}{\rightarrow}$.

(d) Five line segments are $\overline{OE,} \ \overline{OC,} \ \overline{OB,} \ \overline{OD,} \ \overline{DE}$

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

Solution: The name of lines are: $\overline{AB,} \ \overline{AC,} \ \overline{AD,} \ \overline{BC,} \ \overline{BD,} \ \overline{BA,} \ \overline{CD,} \ \overline{CB,} \ \overline{CA,} \ \overline{DC,} \ \overline{DB,} \ \overline{DA}$

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) Line $\underset{AE}{\leftrightarrow}$ and $\underset{EF}{\leftrightarrow}$ contains point E.

(b) Line passing through A is $\underset{AE}{\leftrightarrow}$.

(c) Point O lies on the line $\underset{OC}{\leftrightarrow}$.

(d) $\underset{AE}{\leftrightarrow}$$\underset{EF}{\leftrightarrow}$ and $\underset{AE}{\leftrightarrow}$$\underset{OC}{\leftrightarrow}$ are the two pairs of intersecting lines.

4. How many lines can pass through (a) one given point? (b) two given points?

Solution: (a) Infinite number of lines can pass through the one given point.

(b) One line can pass through the two given points.

5. Draw a rough figure and label suitably in each of the following cases:

(a) Point P lies on $\underset{AB}{\leftrightarrow}$.

(b) $\underset{XY}{\leftrightarrow}$ and $\underset{PQ}{\leftrightarrow}$ intersect at M.

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

(d) $\underset{OP}{\leftrightarrow}$ and $\underset{OQ}{\leftrightarrow}$ meet at O.

Solution: (a)

(b)

(c)

(d)

6. Consider the following figure of line $\underset{MN}{\leftrightarrow}$. 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 $\underset{MN}{\leftrightarrow}$.

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

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

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

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

(f) M is point on ray $\small \underset{OP}{\rightarrow}$ .

(g) Ray $\small \underset{OP}{\rightarrow}$ is different from ray $\small \underset{QP}{\rightarrow}$.

(h) Ray $\small \underset{OP}{\rightarrow}$ is same as ray $\small \underset{OM}{\rightarrow}$ .

(i) Ray $\small \underset{OM}{\rightarrow}$ is not opposite to ray $\small \underset{OP}{\rightarrow}$.

(j) O is not an initial point of $\small \underset{OP}{\rightarrow}$.

(k) N is the initial point of $\small \underset{NP}{\rightarrow}$ and $\small \underset{NM}{\rightarrow}$

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