Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5

# Exercise 4.1

Question 1

Construct the following quadrilaterals.

(i) Quadrilateral ABCD

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

Sol :

Firstly, a rough sketch of this quadrilateral can be drawn as follows.

(Step-1) ΔABC can be constructed by using the given measurements as follows.

(Step-2) Vertex D is 6 cm away from vertex A. Therefore, while taking A as centre, draw an arc of radius 6 cm.

(Step-3) Taking C as centre, draw an arc of radius 4 cm, cutting the previous arc at point D. Join D to A and C.

ABCD is the required quadrilateral.

(ii) Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

Sol :

Firstly, a rough sketch of this quadrilateral can be drawn as follows.

(Step-1) Δ JUP can be constructed by using the given measurements as follows.

(Step-2) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U. Taking P and U as centres, draw arcs of radii 5 cm and 4 cm respectively. Let the point of intersection be M.

(Step-3) Join M to P and U.

JUMP is the required quadrilateral.

(iii) Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

Sol :

We know that opposite sides of a parallelogram are equal in length and also these are parallel to each other.

Hence, ME = OR, MO = ER

A rough sketch of this parallelogram can be drawn as follows.

(Step-1) Δ EOR can be constructed by using the given measurements as follows.

(Step-2) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Therefore, while taking O and E as centres, draw arcs of 4.5 cm radius and 6 cm radius respectively. These will intersect each other at point M.

(Step-3) Join M to O and E.

MORE is the required parallelogram. |

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

Sol :

We know that all sides of a rhombus are of the same measure.

Hence, BE = ES = ST = TB

A rough sketch of this rhombus can be drawn as follows.

(Step-1) Δ BET can be constructed by using the given measurements as follows.

(Step-2) Vertex S is 4.5 cm away from vertex E and also from vertex T. Therefore, while taking E and T as centres, draw arcs of 4.5 cm radius, which will be intersecting each other at point S.

(Step-3) Join S to E and T.

BEST is the required rhombus. |