[tex]\begin{gathered} |XY|\text{ is the midpoint of |UW|} \\ |XY|=\text{ }\frac{1}{2}UW \\ |XY|\text{ = }\frac{1}{2}\text{ x 9} \\ |XY|\text{ = 4.5} \end{gathered}[/tex][tex]\begin{gathered} |VY|\text{ is the midpoint of |VW|} \\ |VY|\text{ = }\frac{1}{2}VW \\ 4=\frac{1}{2}VW \\ |VW|\text{ = 4 x 2} \\ |VW|=8 \end{gathered}[/tex]
Taking Parallelogram XYUZ, we have the following:
[tex]\begin{gathered} |XY|\text{ = |UZ| (Opposite sides of a parrallelogram are congruent i.e equal in length)} \\ |UZ|=4.5 \\ |XU|=|YZ|\text{ (Opposite sides of a parallelogram are equal in length)} \\ |XU|=3 \end{gathered}[/tex]
By Sisilar triangle theorem, we have:
[tex]\begin{gathered} \frac{XV}{XU}=\frac{VY}{YW} \\ \\ \frac{XV}{3}=\frac{4}{8} \\ XV=\frac{3\text{ x 4}}{8} \\ XV=\frac{12}{8} \\ XV=1.5 \end{gathered}[/tex]
Hence,
I) UV=4.5
II)XY=4.5
III)YW=8
IV)XV=1.5
V)ZW=4.5
VI)VW=12
