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.