## Geometry: Common Core (15th Edition)

$x = 2$ $y = 6$
Theorem 6-6 states that in a quadrilateral that is a parallelogram, its diagonals bisect one another. This means that each segment of the bisected diagonal is equal. We can set the two segments of the bisected diagonals equal to one another: $2x = 4$ Divide by $2$ on each side of the equation to solve for $x$: $x = 2$ Let's set the two segments of the other bisected diagonal equal to one another $y - 1 = 2y - 7$ Add $1$ to each side of the equation to isolate constants on one side of the equation: $y = 2y - 6$ Subtract $2y$ from each side of the equation to isolate the variable on the left side of the equation: $-y = -6$ Divide each side of the equation by $-1$ to solve for $y$: $y = 6$