Question

Construct a parallelogram ABCD, in which diagonal AC = 3.8 cm, diagonal BD = 4.6 cm and the angle between AC and BD is 60°.

Answer 1

We know that the diagonals of a parallelogram bisect each other.

Steps of construction:
Step 1: Draw AC= $3.8\mathrm{cm}$
Step 2: Bisect AC at O.
Step 3: Make $\angle COX={60}^{\circ }$
Produce XO to Y.
Step 4:
$$\begin{gathered} OB=\frac{1}{2}(4.6)\mathrm{cm} \\ OB=2.3\mathrm{cm} \\ \mathrm{and}OD=\frac{1}{2}(4.6)\mathrm{cm} \\ OD=2.3\mathrm{cm} \end{gathered}$$
Step 5: Join AB, BC, CD and AD.
​Thus, ABCD is the required parallelogram.