Exercise 4.1 

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Q1. Use the figure to name:

(a) Five points

Solution: The five point of this figure:- B, C, O, E, D

(b) A line

Solution: DB

 (c) Four rays

Solution: OB, OC, OP, OD

(d) Five line segments

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

Q3. Use the figure to name :

Q4. How many lines can pass through

(a) one given point?

Solution: Infinity lines can pass through one point.

(b) Two given points?

Solution: Only one lines can pass through one point.

Q5. Draw a rough figure and label suitably in each of the following cases:.

(a) Point P lies on AB.

Solution:

 

Exercise 4.2 

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Q1. Classify the following curves as (i) Open or (ii) Closed.

Solution: 

(i) Open curves : (a) and (c) 

(ii) Close curves : (b) (d) and (e) 

Q2. Draw rough diagrams to illustrate the following :
(a) Open curve (b) Closed curve.

Solution: 

Q3. Draw any polygon and shade its interior.

Solution: 

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

Solution: 

(a) Is it a curve?

Solution: yes, it is a curve

(b) Is it closed?

Solution: yes, it is a closed

Q5. 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.

Solution: 

(c) A polygon with two sides.

Solution:  The polygon can be made with three or more sides. There is no polygon with two sides.

Exercise 4.3

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Q1. Name the angles in the given figure.

Solution:  Solution:   ∠ADC ,  ∠DCB,  ∠CBA and ∠BAD

Q2. In the given diagram, name the point(s)
(a) In the interior of ∠DOE
(b) In the exterior of ∠EOF
(c) On ∠EOF

(a) In the interior of ∠DOE

Solution: Point A

(b) In the exterior of ∠EOF.

Solution: Point C

(c) On ∠EOF

Solution: Point B

Q3. 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.

Solution: 

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Exercise 4.4 

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Q1. 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?

Solution: 

Q2. (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?

Solution: 

 

Exercise 4.5 

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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?

Solution: 

Diagonals of quadrilateral PQRS are PR and QS 

Meeting Point is O which is interior of quadrilateral PQRS. 

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.

Solution: 

(a) two pairs of opposite sides,

Solution: 

(i) KL and NM

(ii) KN and LM 

(b) two pairs of opposite angles,

Solution: 

(i) ∠K and ∠M 

(ii) ∠L and ∠N
(c) two pairs of adjacent sides,

Solution: 

(i) KN and KL

(ii) KL and ML 

(d) two pairs of adjacent angles. 

Solution: 

(i) ∠K and ∠L

(ii) ∠M and ∠N 

Exercise 4.6 

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Q1. From the figure, identify :

(a) the centre of circle

Solution: The centre of circle is O.  

(b) three radii

Solution: Three radii are OA, OB and OC. 

(c) a diameter

Solution: AC is diameter of circle. 

(d) a chord

Solution: ED is a chord. 
(e) two points in the interior

Solution: Two points in the interior are P and O. 

(f) a point in the exterior

Solution: Q is the point in the exterior of circle. 

(g) a sector

Solution: AOB forms sector.

(h) a segment

Solution: ED forms segment.

Q2. (a) Is every diameter of a circle also a chord?
(b) Is every chord of a circle also a diameter?

Solution:

(a) Yes, every diameter of a circle is also a chord.

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

Q3. 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

Solution: 

(a) its centre : O

(b) a radius : OA 
(c) a diameter : AC

(d) a sector : AOB

(e) a segment : ED

(f) a point in its interior : Point P
(g) a point in its exterior : Point Q

(h) an arc : arch AB 

Q4. Say true or false :
(a) Two diameters of a circle will necessarily intersect.
(b) The centre of a circle is always in its interior.

Solution: 

(a) True

(b) True