The perpendicular distances between the pair of opposite sides of the parallelogram $ABCD$ are $3\text{ cm}$ and $4 \text{cm}$, one of its angles measures $60°$. With the given dimensions using ruler and compasses only, construct the figure of parallelogram $ABCD$.

Draw the figure of Parallelogram $ABCD$ with the following data given, $AB=6 cm, AD=5 cm, \angle DAB=45°.$ Let the sides $AC$ and $DB$ meet at point $O$ and let $E$ be the mid-point of $BC$. Join $OE.$ Prove that $OE\parallel AB.$

Draw the figure of Parallelogram $ABCD$ with the following data given, $AB=6 cm, AD=5 cm, \angle DAB=45°.$ Let the sides $AC$ and $DB$ meet at point $O$ and let $E$ be the mid-point of $BC$. Join $OE.$ Prove that $OE=\frac{1}{2}AB.$