**Class 6 | Mathematics | Chapter 1 | Knowing Our Numbers | NCERT Solut**ions

**Exercise 4.1**

**Question 1**: Use the figure to name:

(a) Five points

(b) A line

(c) Four rays

(d) Five line segments

**Answer 1:**

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

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

**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.

**Question 4:** How many lines can pass though:

(a) one given point?

(b) two given points

** Answer 4:** (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:

Answer:

**Question 6:** Consider the following figure of line MN . Say whether following statements are true or false in the context of the given figure:

** Answer 6:** (a) True (b) True (c) True (d) False (e) False (f) False (g) True (h) False (i) False (j) False (k) True

**Exercise 4.2**

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

**Answer 1:** (a) Open curve (b) Closed curve (c) Open curve (d) Closed curve (e) Closed curve

**Question 2**. Draw rough diagrams to illustrate the following : (a) Open curve (b) Closed curve.

**Answer 2 :**

**a) Open curves**

**b) closed curve**

**Question 3.** Draw any polygon and shade its interior.

**Answer 3:**

**Question 4**. Consider the given figure and answer the questions : (a) Is it a curve? (b) Is it closed?

**Answer 4: **

a) Yes, it is a curve

b) Yes, it is closed.

**Question 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.

**Answer 5 :**

a)

b)

c) Polygon with two sides cannot be draw.

## EXERCISE 4.3

**Question 1.** Name the angles in the given figure.

**Answer 1:** The angles in given figure are : ∠ABC, ∠ CDA, ∠DAB, ∠DCB

**Question 2.** In the given diagram, name the point(s)

(a) In the interior of ∠DOE

(b) In the exterior of ∠EOF (c) On ∠EOF

**Answer 2 :** (a) Point interior of ∠DOE is A

(b) Points exterior of ∠EOF is C, A, D

(c) Points on ∠EOF is E, O, B, F

**Question 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.

**Answer 3 :**

a)

b)

c)

d)

e)

**EXERCISE 4.4 **

**Question 1.** Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?

**Answer 1:**

Point A lies on ΔABC.

**Question 2**. (a) Identify three triangles in the figure.

(b) Write the names of seven angles.

(c) Write the names of six line segments.

(d) Which two triangles have ∠B as common?

**Answer 2 :** (a) The three triangles are: ∠ABC,∠ABD,∠ADC

(b) Angles are:∠ADB, ∠ADC,∠ABD,∠ACD,∠BAD,∠CAD,∠BAC

$\left(c\right)\mathrm{Line}\mathrm{segments}\mathrm{are}:\overline{\mathrm{AB}},\overline{\mathrm{AC}},\overline{\mathrm{AD}},\overline{\mathrm{BD}},\overline{\mathrm{DC}},\overline{\mathrm{BC}}$

(d) Triangles having common∠B: ΔABC, ΔABD,

**EXERCISE 4.5 **

**Question 1.** Draw a rough sketch of a quadrilateral PQRS. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?

**Answer 1 :**

Diagonal : PR and QS

Diagonal meet at point O which is in the interior of quadrilateral PQRS.

**Question 2.** Draw a rough sketch of a quadrilateral KLMN. State,

(a) two pairs of opposite sides,

(b) two pairs of opposite angles,

(c) two pairs of adjacent sides

(d) two pairs of adjacent angles.

**Answer 2 : **

a) (a) Pair of opposite sides : KL and MN, KN and LM

(b) Pair of opposite angles : ∠K and∠M,∠L and∠N

(c) Pair of adjacent sides : KN and NM, KL and LM

(d) Pair of adjacent angles :∠K and∠N,∠L and∠M

## EXERCISE 4.6

**Question 1 :** Take a circular sheet. Fold it into two halves. Crease the fold and open up. Do you find that the circular region is halved by the diameter? A diameter of a circle divides it into two equal parts; each part is a semi-circle. A semi-circle is half of a circle, with the end points of diameter as part of the boundary.

1. From the figure, identify :

(a) the centre of circle

(b) three radii

(c) a diameter

(d) a chord

(e) two points in the interior

(f) a point in the exterior

(g) a sector

(h) a segment

**Answer 1 :** (a) O is the centre.

(b) Three radii: OA, OB and OC

(c) A diameter: AC

(d) A chord: ED

(e) Interior points: O, P

(f) Exterior point: Q

(g) A sector: OAB

(h) A segment: ED

**Question 2.** (a) Is every diameter of a circle also a chord? (b) Is every chord of a circle also a diameter?

**Answer 2 :** (a) Yes, every diameter of a circle is also a chord.

(b) No, every chord of a circle is not a diameter.

3. Draw any circle and mark

(a) its centre

(b) a radius

(c) a diameter

(d) a sector

(e) a segment

(f) a point in its interior

(g) a point in its exterior

(h) an arc

**Answer 3 :**

a) Center : O

b) Radius = OA

c) Diameter = AB

d) Sector = COD

e) Segment = DE

f) O

g) F

h) AC

**Question 4.** Say true or false :

(a) Two diameters of a circle will necessarily intersect.

(b) The centre of a circle is always in its interior.

**Answer 4 :** (a) True

(b) True

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