We want to determine the values for which ABCD is a parallelogram, using the given algebraic expressions for the segment lengths.
Recall the theorem which tells us that if a quadrilateral is a parallelogram, then its opposite sides are congruent. Therefore, the following segments are congruent.
AB ≅ DC and AD ≅ BC
By the definition of congruent segments, we can conclude that their lengths are equal.
AB=DC and AD=BC
Let's create a system of equations by substituting the lengths of the segments into these equations.
7x-2=5x+2 6x+y=7x-1
To solve it we will use the Substitution Method.
