1.Construct the following quadrilaterals.
(i) Quadrilateral LIFT

LI = 4 cm

IF = 3 cm

TL = 2.5 cm

LF = 4.5 cm

IT = 4 cm

(ii) Quadrilateral GOLD

OL = 7.5 cm

GL = 6 cm

GD = 6 cm

LD = 5 cm

OD = 10 cm

(iii) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

(i)Draw a rough sketch first as per the given dimensions.

Construction:

Step 1: Draw a line segment LI = 4 cm.

Step 2: Draw an arc with centre at I and radius 3 cm.

Step 3: Draw another arc with centre L and radius 4.5 cm to meet the former arc at F and Join LF and IF.

Step 4: Draw an arc with centre L and radius 2.5 cm.

Step 5: Draw another arc with centre I and radius 4 cm to meet the previous arc at T and Join LT and IT.

Hence we have LIFT as the required quadrilateral with given dimensions.

(ii)Draw a rough sketch first as per the given dimensions.


Construction:

Step 1: Draw a line segment OL = 7.5 cm

Step 2: Draw an arc with centre at O and of radius 10 cm.

Step 3: Draw another arc with centre at L and of radius 5 cm to meet the previous arc at D and join OD and LD.

Step 4: Draw an arc with centre L and D with equal radii of 6 cm to meet each other at G and join LG and DG.

Hence we have GOLD as the required quadrilateral with given dimensions.

(iii)Draw a rough sketch first as per the given dimensions and we know that the diagonals of a rhombus bisect each other at the right angle.


Construction:

Step 1: Draw a line segment BN = 5.6 cm.

Step 2: Draw the right bisector of BN at O.

Step 3: Draw two arcs with centre O and radius \(\frac { 1 }{ 2 } \times DE\), i.e., \(\frac { 1 }{ 2 } \times 6.5 = 3.25 cm\) to meet the right bisector at D and E.

Step 4: Join BE, EN, ND and BD.

Hence we have, BEND as the required rhombus with given dimensions.