**Practical Geometry**

**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°

**Solution.****(i)** Let us draw a rough sketch of the required quadrilateral and write down the given dimensions.**Steps of Construction :**

- Draw EA = 5 cm.
- Make ∠XEA = 60°.
- With E as centre and radius 4 cm, cut off ED = 4 cm along EX.
- Make ∠EAY = 90°.
- With A as centre and radius 4.5 cm, draw an arc to cut off AY at R.
- Join DR.

Then, DEAR is the required quadrilateral.

**(ii)** Let us draw a rough sketch of the required quadrilateral and write down the given 3 5 cm dimensions.**Steps of Construction :**

- Draw RU = 3 cm.
- Make ∠URX = 75°.
- With R as centre and radius 3.5 cm, cut off RT = 3.5 cm along RX.
- Make ∠RUY =120°
- With U as centre and radius 4 cm, draw an arc to cut CY at E Join TE.
- Then, TRUE is the required quadrilateral.