Question

Show that a quadrilateral with the given vertices is a parallelogram. Find the length of each side. Round your answer to two decimal places if necessary.

Answer 1

A parallelogram has opposite sides parallel and equal

Side VU = 5 units and ST = 5 units

VU = ST

Next find the length of VS and UT

Apply Pythagoras theorem to find the length of VS

`\begin{gathered} \text{Hypotenuse = VS} \\ \text{Opposite = 4} \\ \text{Adjacent = 1} \\ \text{Opposite}^2+Adjacent^2=Hypotenuse^2 \\ 4^2+1^2=VS^2 \\ 16+1=VS^2 \\ VS^2\text{ = 17} \\ VS\text{ = }\sqrt[]{17} \\ VS\text{ = 4.12} \end{gathered}`

Side VS = Side UT

since opposite sides are equal and parallel, VUTS is a parallelogram.