Construct a parallelogram ABCD, if :

lengths of diagonals AC and BD are 5.4 cm and 6.7 cm respectively, and the angle between them is 60°.

Steps:

1. Draw BD = 6.7 cm.

2. Locate the mid-point O of BD by drawing its perpendicular bisector.

3. Through O, construct a line EOF so that angle EOD = 60°.

4. From EF, cut OC = $\dfrac{AC}{2}$ = $\dfrac{5.4}{2}$ = 2.7 cm and also OA = $\dfrac{AC}{2}$ = $\dfrac{5.4}{2}$ = 2.7 cm

5. Join AB, BC, CD and DA.

Hence, ABCD is the required parallelogram.