Construct the following quadrilaterals,

(i) Quadrilateral DEAR

DE = 4 cm

EA = 5 cm

AR = 4.5 cm

∠E = 60°

∠A = 90°

(ii) Quadrilateral TRUE

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

∠R = 75°

∠U = 120°

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Solution

(i)

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

(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.

(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.

(4) Join D to R.

DEAR is the required quadrilateral.

(ii)

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

(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.

(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.

(4) Join T to E.

TRUE is the required quadrilateral.

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Similar questions

Construct the quadrilateral $D E A R$ where $D E = 4 c m, E A = 5 c m, A R = 4.5 c m, ∠ E = 60^{\circ}, ∠ A = 90^{\circ}$

Question 1
Construct the Quadrilateral DEAR where
DE=4cm, EA=5cm, AR=4.5cm, $∠ E = 60^{\circ}, ∠ A = 90^{\circ}$

∠ R = 75 °

∠ U = 120 °

3.5 c m

3 c m

4 c m

∠ R = 75^{\circ}

∠ U = 120^{\circ}

Construct a quadrilateral ABCD in which: $∠ A = 120^{\circ}, ∠ B = 60^{\circ}, ∠ AB = 4 c m, B C = 4.5 c m and C D = 5 c m .$

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