Construct the following quadrilaterals.

(i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

 

(ii) Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

 

(iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

(i) The steps of construction are: 

Step (a) Draw a line segment MO of 6 cm and an angle of 105° at point O.

As vertex R is 4.5 cm away from the vertex O, therefore, cut a line segment OR of 4.5 cm from this ray

Step (b) Now, draw an angle of 105° at point R

Step (c) Draw an angle of 60° at point M and this ray meet the previously drawn ray from R at point E

Thus, MORE is the required quadrilateral, as given below, 

(ii) As we know that the sum of the angles of a quadrilateral is 360°

In quadrilateral PLAN,

∠ P + ∠ L + ∠ A + ∠ N = 360°

90° + ∠ L + 110° + 85° = 360°

285° + ∠ L = 360°

∠ L = 360° - 285°

= 75°

The steps of construction are: 

Step (a) Draw a line segment PL of 4 cm and also draw an angle of 75° at point L. Vertex A is 6.5 cm away from vertex L so cut a line segment LA of 6.5 cm from this ray

Step (b) From point A draw an angle of 110°

Step (c) Draw an angle of 90° at point P. This ray will meet the previously drawn ray from A at point N

Thus, the required quadrilateral is shown below: 

(iii) The steps of construction are: 

Step (a) Draw a line segment HE of 5 cm and an angle of 85° at point E.

Vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray

Step (b) Vertex R is 6 cm and 5 cm away from vertex H and A respectively.

So by taking radius as 6 cm and 5 cm, draw arcs from point H and A respectively. These will intersect each other at point R

Step (c) Join R to H and A

Thu, the required quadrilateral is shown below: 

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

Step (a) Draw a line segment OK of 7 cm and an angle of 90° at point K

Vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray

Step  (b) Vertex Y is of 5 cm and 7 cm away from vertex O and A respectively. Now by taking 5 cm and 7 cm as radius draw arcs from point O and A respectively and these will intersect at point Y

Step  (c) Join Y to A and O

Thus, the required quadrilateral is shown below: