Question

Use ruler and compasses to construct a parallelogram with diagonals 6 cm and 8 cm in length having given the acute angle between them is ${60}^{\circ }$.

Answer 1

Both diagonals of parallelogram are given then take AC = 8cm and BD = 6m.

Steps of construction :

$\Rightarrow$ Draw a line segment AC = 8cm.

$\Rightarrow$ With center A and radius more than half of AC, draw arcs, one on each sides of AC.

$\Rightarrow$ With center B and same radius, draw arcs cutting the previous arcs P and Q respectively.

$\Rightarrow$ Join PQ which is perpendicular to BC and bisects BC at half.

$\Rightarrow$ Construct an angle 60${}^{\circ }$ at O on both sides of AC that is above and below.

$\Rightarrow$ Then draw the line through an angles which will be passing through pint O.

$\Rightarrow$ Cut off OD = 3cm and OB = 3cm. Then we get DB = 6cm.

$\Rightarrow$ Join AD, DC, BC and BA.

Thus, ABCD is the required parallelogram.