Solution of Chapter 4 Basic Geometrical Ideas Class 6th Mathematics (2023-24)

                                                                                               Exercise 4.1 

1. Use the figure to name:

(a) Five points

(b) A-line

(c) Four rays

(d) Five line segments

Solutions:

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

(b) A line is 

(c) Four rays are , , and .

(d) Five line segments are , , , and 

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

Solutions:

The lines are , , , , , , , , , , , 

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.

Solutions:

(a) Line containing point E is 

(b) Line passing through A is 

(c) Line on which O lies is 

(d) Two pairs of intersecting lines are , and , 

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

Solutions:

(a) Countless lines can pass through a given point.

(b) Only one line can pass through two given points.

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

(a) Point P lies on .

(b)  and  intersect at M.

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

(d)  and  meet at O.

Solutions:

(a)

(b)

(c)

(d)

6. 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 .

(b) M, O, N are points on a line segment .

(c) M and N are end points of line segment.

(d) O and N are end points of line segment .

(e) M is one of the end points of line segment .

(f) M is point on ray .

(g) Ray
 is different from ray .

(h) Ray  is same as ray .

(i) Ray  is not opposite to ray .

(j) O is not an initial point of 

(k) N is the initial point of  and .

Solutions:

(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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                                                                                             Exercise 4.2 

1. Classify the following curves as (i) Open or (ii) Closed

Solutions:

(a) The given curve is an open curve

(b) The given curve is a closed curve

(c) The given curve is an open curve

(d) The given curve is a closed curve

(e) The given curve is a closed curve

2. Draw rough diagrams to illustrate the following:

(a) Open curve

(b) Closed curve

Solutions

(a) The below figure is an open curve

(b) The below figure is a closed curve

3. Draw any polygon and shade its interior.

Solutions:

The below figure is a polygon with a shaded interior.

4. Consider the given figure and answer the questions:

(a) Is it a curve?

(b) Is it closed?

Solutions:

(a) Yes, it is a curve

(b) Yes, it is a closed curve

5. Illustrate, if possible, each one of the following with a rough diagram:

(a) A closed curve that is not a polygon.

(b) An open curve made up entirely of line segments.

(c) A polygon with two sides.

Solutions:

(a) The below figure is a closed figure but not a polygon.

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

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

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                                                                                                     Exercise 4.3 

1. Name the angles in the given figure.

Solutions:

The angles are ∠DAB, ∠ABC, ∠BCD and ∠CDA

2. In the given diagram, name the points(s)

(a) In the interior of ∠DOE

(b) In the exterior of ∠EOF

(c) On ∠EOF

Solutions:

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

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

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

3. Draw rough diagrams of two angles such that they have

(a) One point in common

(b) Two points in common

(c) Three points in common

(d) Four points in common

(e) One ray in common

Solutions:

(a) O is the common point between ∠COD and ∠AOB

(b) O and B are common points between ∠AOB and ∠BOC

(c) O, E and B are common points between ∠AOB and ∠BOC

(d) O, E, D and A are common points between ∠BOA and ∠COA

(e) OC is a common ray between ∠BOC and ∠AOC