Use ruler and compasses construct a parallelogram with diagonals $6 \mathrm{cm}$ and $8 \mathrm{cm}$ in length having given the acute angle between them is ${60}^{°}$. Measure one of the longest sides.

Construct a trapezium $\mathrm{PQRS}$ where $\mathrm{PQ}\parallel \mathrm{RS}$ and $\mathrm{PQ}=7.5 \mathrm{cm}, \mathrm{QR}=4 \mathrm{cm}, \mathrm{RS}=3 \mathrm{cm}$ and $\mathrm{SP}=3.5 \mathrm{cm}$. Also, measure $\angle \mathrm{QPS}$.

Given the quadrilateral below, what value of $x$would allow you to conclude that the figure is a parallelogram? 

In the figure, if $\mathrm{ABCD}$is a rectangle, what type of triangle must $△\mathrm{ABD}$be?