question_answer 4)

                Construct the following quadrilaterals: (i) Quadrilateral DEAR DE = 4 cm EA = 5 cm AR = 4.5 cm \[\angle E={{60}^{o}}\] \[\angle A={{90}^{o}}\] (ii) Quadrilateral TRUE TR = 3.5 cm RU = 3 cm UE = 4 cm \[\angle R={{75}^{o}}\] \[\angle U={{120}^{o}}\]

Answer:

                (i) Steps of Construction 1. Draw DE = 4 cm. 2. At E, draw ray EX such that \[\angle DEX={{60}^{o}}\] 3. From ray EX, cut EA = 5 cm. 4. At A, draw ray AY such that \[\angle EAY={{90}^{\text{o}}}\]. 5. Cut AR = 4.5 cm from ray AY. 6. Join RD. Then, DEAR is the required quadrilateral. (ii) Steps of Construction 1. Draw TR = 3.5 cm. 2. At R, draw ray RX such that \[\angle TRX={{75}^{\text{o}}}\]. 3. Cut RU = 3 cm from ray RX. 4. At U, draw ray UY such that \[\angle RUY={{120}^{\text{o}}}\]. 5. Cut UE = 4 cm from ray UY. 6. Join ET. Then, TRUE is the required quadrilateral.