We want to find the values of a and b for the parallelogram WXZY, using the given algebraic expressions for the segment lengths. For convenience, we will label the point of intersection of the diagonals T.
If a quadrilateral is a parallelogram, then the diagonals bisect each other.
Therefore, the following segments are congruent.
WT ≅ TZ and YT ≅ TX
By the definition of congruent segments, we can conclude that their lengths are equal.
WT = TY and ZT = TX
Let's create two equations by substituting the lengths of the segments into these equations.
2=a-7 and 10=2b-6
Let's start by solving the first equation for a.
