Exercise 4.1 Exercise 4.2 Exercise 4.3 Exercise 4.4 Exercise 4.5

# Exercise 4.4

Question 1

Construct the following quadrilaterals,

(i) Quadrilateral DEAR

DE = 4 cm

EA = 5 cm

AR = 4.5 cm

∠E = 60°

∠A = 90°

Sol :

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

(Step-2) Draw a line segment DE of 4 cm and an angle of 60º at point E. As vertex A is 5 cm away from vertex E, cut a line segment EA of 5 cm from this ray.

(Step-3) Again draw an angle of 90º at point A. As vertex R is 4.5 cm away

from vertex A, cut a line segment RA of 4.5 cm from this ray.

(Step-4) Join D to R.

DEAR is the required quadrilateral.

(ii) Quadrilateral TRUE

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

∠R = 75°

∠U = 120°

Sol :

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

(Step-2) Draw a line segment RU of 3 cm and an angle of 120º at point U. As vertex E is 4 cm away from vertex U, cut a line segment UE of 4 cm

from this ray.

(Step-3) Next, draw an angle of 75º at point R. As vertex T is 3.5 cm away from vertex R, cut a line segment RT of 3.5 cm from this ray.

(Step-4) Join T to E.

TRUE is the required quadrilateral.