Question

If DH = 2z - 31 and FH=z, find the value of z that makes quadrilateral DEFG a parallelogram.

Answer 1

`z=31`

Step-by-step explanation

We want to find the value of z for which DEFG is a parallelogram.

For DEFG to be a parallelogram, its diagonals must bisect one another. This implies that:

`DH=FH`

Therefore:

`2z-31=z`

Solve for z:

`\begin{gathered} 2z-z=31 \\ z=31 \end{gathered}`

That is the value of z for which DEFG is a parallelogram.