question_answer 3)

                Construct the following quadrilaterals: (i) Quadrilateral MORE MO = 6 cm OR = 4.5 cm \[\angle M={{60}^{\text{o}}}\] \[\angle O={{105}^{\text{o}}}\] \[\angle R={{105}^{\text{o}}}\] (ii) Quadrilateral PLAN PL = 4 cm LA = 6.5 cm \[\angle P={{90}^{\text{o}}}\] \[\angle A={{110}^{\text{o}}}\] \[\angle N={{85}^{\text{o}}}\] (iii) Parallelogram HEAR HE = 5 cm EA = 6 cm \[\angle R={{85}^{\text{o}}}\] (iv) Rectangle OKAY OK = 7cm KA = 5 cm.

Answer:

                (i) Steps of Construction 1. Draw MO = 6 cm. 2. At O, draw ray OX such that \[\angle MOX={{105}^{\text{o}}}\]. 3. Cut OR = 4.5 cm from ray OX. 4. At M, draw ray MY such that \[\angle OMY={{60}^{\text{o}}}\]. 5. At R, draw ray RZ such that \[\angle ORZ={{105}^{\text{o}}}\]. Let the rays MY and RZ meet at E. Then, MORE is the required quadrilateral. (ii) Steps of Construction 1. Draw PL = 4 cm. 2. At L, draw ray LX such that \[\angle PLX={{75}^{\text{o}}}\] By Angle-sum property of quadrilateral, \[\angle P+\angle A+\angle N+\angle L={{360}^{\text{o}}}\] \[\Rightarrow \]               \[{{90}^{\text{o}}}+{{110}^{\text{o}}}+{{85}^{\text{o}}}+\angle L={{360}^{\text{o}}}\] \[\Rightarrow \]               \[{{285}^{\text{o}}}+\angle L={{360}^{\text{o}}}\] \[\Rightarrow \]               \[\angle L={{360}^{\text{o}}}-{{285}^{\text{o}}}\] \[\Rightarrow \]               \[\angle L={{75}^{\text{o}}}\] 3. Cut LA = 6.5 cm from ray LX. 4. At A, draw ray AY such that \[\angle LAY={{110}^{\text{o}}}\]. 5. At P, draw ray PZ such that \[\angle LPZ={{90}^{\text{o}}}\]. Let the rays AY and PZ meet at N. Then, PLAN is the required quadrilateral. (iii) Steps of Construction 1. Draw HE = 5 cm. 2. At E, draw ray EX such that \[\angle HEX={{85}^{\text{o}}}\] |Opposite angles of a parallelogram are equal. 3. Cut EA = 6 cm from the ray EX. 4. With A as centre and radius AR = 5 cm, draw an arc. 5. With H as centre and radius HE = 6 cm, draw another arc to intersect the arc of step 4 at R. 6. Join AR and HE. Then, HEAR is the required parallelogram. (iv) Steps of Construction 1. Draw OK = 7 cm. 2. At K, draw ray KX such that \[\angle OKX={{90}^{\text{o}}}\]. 3. Cut KA = 5 cm from ray KX. 4. Taking A as centre and radius AY = 7 cm, draw an arc. 5. Taking O as centre and radius OY = 5 cm, draw another arc to intersect the arc of step 4 at Y. 6. Join AY and OY. Then OKAY is the required rectangle.