Use ruler and compasses to construct a paralle- logram with diagonals 6 cm and 8 cm in length having given the acute angle between them is 60°. Measure one of the longer sides. (ICSE)
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Both diagonals of parallelogram are given then take AC = 8cm and BD = 6m.
Steps of construction :
⇒ Draw a line segment AC = 8cm.
⇒ With center A and radius more than half of AC, draw arcs, one on each sides of AC.
⇒ With center B and same radius, draw arcs cutting the previous arcs P and Q respectively.
⇒ Join PQ which is perpendicular to BC and bisects BC at half.
⇒ Construct an angle 60
∘
at O on both sides of AC that is above and below.
⇒ Then draw the line through an angles which will be passing through pint O.
⇒ Cut off OD = 3cm and OB = 3cm. Then we get DB = 6cm.
⇒ Join AD, DC, BC and BA.
Thus, ABCD is the required parallelogram.
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