  Question

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

Solution

1)1. Draw $$MO$$ of length $$6$$ cm.2. Draw an angle of $$105$$ degree on $$O$$ and cut an arc of $$4.5$$ cm on it. The point of intersection is $$R$$.3. Draw an angle of $$105$$ degree on $$R$$ and draw an angle of $$60$$ degree on $$M$$. Their point of intersection is $$E$$.4. Join all the points.$$MORE$$ is the required quadrilateral.2)1. Draw $$PL$$ of length $$4$$ cm.2. Calculate the value of $$\angle L$$, which comes out to be $$75^{o}$$.Draw an angle of $$75^{o}$$ on $$L$$ and cut an arc of $$6.5$$ cm on it. The point of intersection is $$A$$.3. Draw an angle of $$110^{o}$$ on $$A$$ and draw an angle of $$90^{o}$$ on $$P$$. Their point of intersection is $$N$$.4. Join all the points.$$PLAN$$ is the required quadrilateral.3) 1. Draw $$EA$$ of length $$6$$ cm.2. Draw an angle of $$85^{o}$$ on $$E$$ and cut an arc of $$5$$ cm on it. The point of intersection is $$H$$. ($$\angle R= \angle E = 85^o$$ and $$\angle H = 95^o$$)3. Draw an angle of $$95^{o}$$ on $$H$$ and cut an arc of $$6$$ cm. Their point of intersection is $$R$$.4. Join all the points.$$HEAR$$ is the required parallelogram.4)1. Draw $$OK$$ of length $$7$$ cm.2. Draw an angle of $$90^{o}$$ on $$K$$ and cut an arc of $$5$$ cm on it. The point of intersection is $$A$$.3. Draw an angle of $$90^{o}$$ on $$A$$ and cut an arc of $$7$$ cm from $$A$$. The point of intersection is $$Y$$.4. Join all the points.$$OKAY$$ is the required rectangle. MathematicsNCERTStandard VIII

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