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:


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