Construct the following quadrilaterals

(i) Quadrilateral ABCD

AB = 4.5 cm

BC = 5.5 cm

CD = 4 cm

AD = 6 cm

AC = 7 cm

(ii) Quadrilateral JUMP

JU = 3.5 cm

UM = 4 cm

MP = 5 cm

PJ = 4.5 cm

PU = 6.5 cm

(iii) Parallelogram MORE

OR = 6 cm

RE = 4.5 cm

EO = 7.5 cm

(iv) Rhombus BEST

BE = 4.5 cm

ET = 6 cm

(i) The rough sketch of this quadrilateral:

(a) ΔABC can be constructed as follows:

(b) Vertex D is 6 cm away from vertex A.

Hence, while taking A as centre, draw an arc of radius 6 cm

(c) Taking C as centre, draw an arc of radius 4 cm which cuts the previous arc at point D. Now, Join D to A and C

ABCD is the required quadrilateral

(ii) The rough sketch of this quadrilateral:

(a) Δ JUP can be constructed as follows:

(b) Vertex M is 5 cm away from vertex P and 4 cm away from vertex U

Now, Taking P and U as centers draw arcs of radii 5 cm and 4 cm respectively. Let the point of intersection be M

(c) Now, Join M to P and U

Hence, JUMP is the required quadrilateral

(iii) As we all know that opposite sides of a parallelogram are not only equal in length but also are parallel to each other

Therefore,

ME = OR,

MO = ER

The rough sketch of this parallelogram:

(a) Δ EOR can be constructed as follows:

(b) Vertex M is 4.5 cm away from vertex O and 6 cm away from vertex E. Hence, while taking O and E as centers, draw arcs of 4.5 cm radius and 6 cm radius respectively

Let, these will intersect each other at point M

(c) Join M to O and E

Therefore, MORE is the required parallelogram

(iv) As we all know that all sides of a rhombus are of the same measure

Therefore,

BE = ES = ST = TB

A rough sketch of this rhombus is as follows:

(a) Δ BET can be constructed as follows:

(b) Vertex S is 4.5 cm away from vertex E and also from vertex T.

Hence, taking E and T as centers, draw arcs of 4.5 cm radius, which will intersect each other at point S

(c) Join these intersected arcs, we will get the required rhombus