Question

Using ruler and compasses only, construct a rectangle each of whose diagonals measures 6 cm and the diagonals intersect at an angle of ${45}^{\circ }$.

Answer 1

Diagonals of a rectangle is given which is 6cm and acute angle between the diagonals are 45${}^{\circ }$

Let AC = BD = 6cm.

Steps of construction :

$\Rightarrow$ Draw a line segment AC = 6cm

$\Rightarrow$ With center A and radius more than half of AC, draw an 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 45${}^{\circ }$ at O on both sides of AC that is above and below with respect to A an C.

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

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

Thus, ABCD is the required rectangle.