Question

Please help with question 3Show that each quadrilateral is a parallelogram for the given values of the variables

Answer 1

Explanation

We are required to show that the given quadrilateral below is a parallelogram:

This is achieved thus:

We know that one of the properties of a parallelogram is that its diagonals bisect each other. Therefore, we have:

`\begin{gathered} |JN|=|NL| \\ 2x+2=4x-10 \\ \text{ Collect like terms} \\ 4x-2x=2+10 \\ 2x=12 \\ (2x)/(2)=(12)/(2) \\ x=6 \end{gathered}`

Also, we have:

`\begin{gathered} |MN|=|NK| \\ 6y+1=8y-6 \\ \text{ Collect like terms } \\ 8y-6y=1+6 \\ 2y=7 \\ (2y)/(2)=(7)/(2) \\ y=3.5 \end{gathered}`

Hence, the quadrilateral is a parallelogram since the values of x and y corresponds to the given.

`x=6;y=3.5`