Question

Based on the diagram, find the following lengths:V4Хy3wUV =XV =XY =ZW=YW =WW=

Answer 1

`\begin{gathered} |XY|\textUW \\ |XY|=\text{ }(1)/(2)UW \\ |XY|\text{ = }(1)/(2)\text{ x 9} \\ |XY|\text{ = 4.5} \end{gathered}`
`\begin{gathered} |VY|\text is the midpoint of \\ |VY|\text{ = }(1)/(2)VW \\ 4=(1)/(2)VW \\ |VW|\text{ = 4 x 2} \\ |VW|=8 \end{gathered}`

Taking Parallelogram XYUZ, we have the following:

`\begin{gathered} |XY|\text (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}`

By Sisilar triangle theorem, we have:

`\begin{gathered} (XV)/(XU)=(VY)/(YW) \\ \\ (XV)/(3)=(4)/(8) \\ XV=\frac{3\text{ x 4}}{8} \\ XV=(12)/(8) \\ XV=1.5 \end{gathered}`

Hence,

I) UV=4.5

II)XY=4.5

III)YW=8

IV)XV=1.5

V)ZW=4.5

VI)VW=12