We want to find the values of x and y for which the given quadrilateral is a parallelogram, using the given algebraic expressions for the lengths of the half-diagonals.
If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.
Therefore, for the quadrilateral to be a parallelogram, the segments with the following lengths are congruent.
4y-9 = 2y+5 and y+3 = 2x+6
Let's create a system of equations by substituting the lengths of the segments into these equations.
4y-9=2y+5 y+3=2x+6
To solve it we will use the Substitution Method.
