## Chapter 4 Practical Geometry 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°

ii) Quadrilateral TRUE

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

∠R = 75°

∠U = 120°

Answer:

i)

Given

Quadrilateral DEAR

DE = 4 cm

EA = 5 cm

AR = 4.5 cm

∠E = 60°

∠A = 90°

Rough figure

Actual figure

Steps of Construction

1. Draw line segment AE = 5 cm.

2. Make ∠YEA= 90°.

3. Make ∠XEA = 60°.

4. With A as centre, radius 4.5 cm draw an arc to cut ray AY at R.

5. With E as centre radius 4 cm draw an arc to cut ray EX at D.

6. Join R and D.

7. DEAR is the required quadrilateral.

ii)

Given

Quadrilateral TRUE

TR = 3.5 cm

RU = 3 cm

UE = 4 cm

∠R = 75°

∠U = 120°

Rough figure

Actual figure

Steps of Construction

1. Draw line segment UR = 3 cm.

2. Make ∠YUR = 120°.

3. Make ∠XRU = 75°.

4. With U as centre, radius 4 cm draw an arc to cut ray YU at E.

5. With R as centre, radius 3.5 cm draw an arc to cut ray XR at T.

6. Join E and T.

7. TRUE is the required quadrilateral.

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