NCERT Solutions: Basic Geometrical Ideas

Exercise 4.1

Q1. Use the figure to name:

(a) Five points
(b) A line
(c) Four rays
(d) Five line segments
Ans:

Q2. Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Ans:



Q3. Use the figure to name:

(a) Line containing point E.
Ans: A line containing

(b) Line passing through A.
Ans: A line passing through

(c) Line on which O lies.
Ans: A line on which O lies

(d) Two pairs of intersecting lines.
Ans: Two pairs of intersecting lines are

Q4. How many lines can pass through 
(a) one given point?
Ans: Infinite number of lines can pass through one given point.

(b) Two given points?
Ans: Only one line can pass through two given points. 

Q5. Draw a rough figure and label suitably in each of the following cases:
(a) Point P lies on .
(b)  intersect at M.
(c) Line l contains E and F but not D.
(d)  meet at O.
Ans:

Q6. Consider the following figure of line  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 
Ans: True

(b) M, O, N are points on a line segment 
Ans: True

(c) M and N are end points of line segment 
Ans: True

(d) O and N are end points of line segment 
Ans: False

(e) M is one of the end points of line segment 
Ans: False

(f) M is point on ray 
Ans: False

(g) Ray   is different from ray 
Ans: True

(h) Ray  is same as ray 
Ans: False

(i) Ray is not opposite to ray 
Ans: False

(j) O is not an initial point of 
Ans: False

(k) N is the initial point of  and  

Ans: True

Exercise 4.2

(a)
Ans: Open curve

(b)
Ans: Closed curve

(c)
Ans: Open curve

(d)
Ans: Closed curve

(e)
Ans: Closed curve

Q2. Draw rough diagrams to illustrate the following:
(a) Open curve
Ans: Open curves

(b) Closed curve
Ans: Closed curves

Q3. Draw any polygon and shade its interior. 
Ans: Polygon ABCDE

Q4. Consider the given figure and answer the questions:
(a) Is it a curve? 
(b) Is it closed?

Ans: (a) Yes, it is a curve.
(b) Yes, it is closed.

Q5. Illustrate, if possible, each one of the following with a rough diagram:
(a) A closed curve that is not a polygon.
Ans:  The below figure is a closed figure but not a polygon.

(b) An open curve made up entirely of line segments.
Ans: The below figure is an open curve made up entirely of line segments.

(c) A polygon with two sides.
Ans: No, it's not possible, as the polygon with the least number of sides is a triangle, which has three sides.

Exercise 4.3

Q1. Name the angles in the given figure.

Ans: There are four angles in given figure:
∠ ABC, ∠ CDA, ∠ DAB, ∠ DCB

Q2. In the given diagram, name the point(s)

(a) In the interior of ∠DOE
Ans: The point in the interior of ∠DOE is A

(b) In the exterior of ∠EOF
Ans: The points in the exterior of ∠EOF is C, A and D

(c) On ∠EOF
Ans: The points on ∠EOF are E, B, O and F

Q3. Draw rough diagrams of two angles such that they have
(a) One point in common.
Ans: O is the common point between ∠COD and ∠AOB

(b) Two points in common.
Ans: O and B are common points between ∠AOB and ∠BOC

(c) Three points in common.
Ans: O, E and B are common points between ∠AOB and ∠BOC

(d) Four points in common.
Ans: O, E, D and A are common points between ∠BOA and ∠COA

(e) One ray in common.
Ans: OC is a common ray between ∠BOC and ∠AOC