Chapter - 4 Basic Geometrical Ideas

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Basic Geometrical Ideas


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,}{
ightarrow} underset{OB,}{
ightarrow}  underset{OC,}{
ightarrow}  underset{OE}{

(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) 






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}{
ightarrow} .

(g) Ray small underset{OP}{
ightarrow} is different from ray small underset{QP}{

(h) Ray small underset{OP}{
ightarrow} is same as ray small underset{OM}{
ightarrow} .

(i) Ray small underset{OM}{
ightarrow} is not opposite to ray small underset{OP}{

(j) O is not an initial point of small underset{OP}{

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

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



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