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Question

Using ruler and compasses only, construct the quadrilateral $$ABCD$$ in which $$ \angle BAD = 45^{o}$$, $$AD = AB = 6cm, BC = 3.6cm, CD = 5cm. $$Measure $$\angle BCD.$$


Solution

Steps of construction:
(i) Draw a line segment $$AB = 6cm$$
(ii)At $$A$$, draw a ray $$AX$$ making an angle of $$45^{o}$$ and cut off $$AD = 6cm$$
(iii)With centre $$B$$ and radius $$3.6 cm$$ and with centre $$D$$ and radius $$5 cm$$, draw two arcs intersecting each other at $$C$$.
(iv) Join $$BC$$ and $$DC$$.
Thus, $$ABCD$$ is the required quadrilateral.
On measuring $$\angle BCD$$, it is $$60^{o}$$
1729221_1810978_ans_b65681ad206d483fbad6157ff671c3ac.PNG

Mathematics

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