Question

Show that each quad trilateral is a parallelogram for the given values of the variables

Answer 1

Given the quadrilateral JKLM

x = 6, y = 3.5

We will prove the diagonals bisect each other by substitution with x, y

`\begin{gathered} 2x+2=2(6)+2=14 \\ 4x-10=4(6)-10=14 \\ So,2x+2=4x-10 \\ \\ 8y-6=8(3.5)-6=22 \\ 6y+1=6(3.5)+1=22 \\ so,8y-6=6y+1 \end{gathered}`

As a result, the diagonals bisect each other

so, the quadrilateral is a parallelogram