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Diagonals of a Parallelogram

The diagonals of a parallelogram bisect each other.

In other words the diagonals intersect each other at the half-way point.

$\begin{array}{|lrcll|} \hline (1) & DH &=& HF \\ & x+1 &=& 3y \\ & x &=& 3y - 1 \\\\ (2) & GH &=& HE \\ & 3x-4 &=& 5y+1 \\ & 3(3y-1) - 4 &=& 5y+1 \\ & 9y-3 - 4 &=& 5y+1 \\ & 9y-7 &=& 5y+1 \quad & | \quad +7-5y\\ & 4y &=& 8 \quad & | \quad : 4 \\ & \mathbf{y} & \mathbf{=} & \mathbf{2} \\\\ (1) & x &=& 3y - 1 \\ & x &=& 3\cdot 2 - 1 \\ & x &=& 6 - 1 \\ & \mathbf{x} & \mathbf{=} & \mathbf{5} \\ \hline \end{array}$