Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5

# Exercise 4.3

Question 1

Construct the following quadrilaterals.

(i) Quadrilateral MORE

MO = 6 cm

OR = 4.5 cm

∠M = 60°

∠O = 105°

∠R = 105°

Sol :

(Step-1)A rough sketch of this quadrilateral can be drawn as follows.

(Step-2) Draw a line segment MO of 6 cm and an angle of 105º at point O. As vertex R is 4.5 cm away from the vertex O, cut a line segment OR of 4.5 cm from this ray.

(Step-3) Again, draw an angle of 105º at point R.

(Step-4) Draw an angle of 60º at point M. Let this ray meet the previously drawn ray from R at point E.

MORE is the required quadrilateral. |

(ii) Quadrilateral PLAN

PL = 4 cm

LA = 6.5 cm

∠P = 90°

∠A = 110°

∠N = 85°

Sol :

(Step-1)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°

(Step-2)A rough sketch of this quadrilateral is as follows.

(Step-3) Draw a line segment PL of 4 cm and draw an angle of 75º at point L. As vertex A is 6.5 cm away from vertex L, cut a line segment LA of 6.5 cm from this ray.

(Step-4) Again draw an angle of 110º at point A.

(Step-5) Draw an angle of 90º at point P. This ray will meet the previously drawn ray from A at point N.

PLAN is the required quadrilateral.

(iii) Parallelogram HEAR

HE = 5 cm

EA = 6 cm

∠R = 85°

Sol :

(Step-1)Firstly, a rough sketch of this quadrilateral is as follows.

(Step-2) Draw a line segment HE of 5 cm and an angle of 85º at point E. As vertex A is 6 cm away from vertex E, cut a line segment EA of 6 cm from this ray.

(Step-3) Vertex R is 6 cm and 5 cm away from vertex H and A respectively. By taking radius as 6 cm and 5 cm, draw arcs from point H and A respectively. These will be intersecting each other at point R.

- Join R to H and A.

HEAR is the required quadrilateral.

(iv) Rectangle OKAY

OK = 7 cm

KA = 5 cm

Sol :

(iv)

(Step-1)A rough sketch of this quadrilateral is drawn as follows.

(Step-2) Draw a line segment OK of 7 cm and an angle of 90º at point K. As vertex A is 5 cm away from vertex K, cut a line segment KA of 5 cm from this ray.

(Step-3) Vertex Y is 5 cm and 7 cm away from vertex O and A respectively. By taking radius as 5 cm and 7 cm, draw arcs from point O and A respectively. These will be intersecting each other at point Y.

(Step-4) Join Y to A and O.

OKAY is the required quadrilateral.