We want to find the values of x and y for which ABCD is a parallelogram, using the given algebraic expressions for the segment lengths.
Recall the theorem referenced in the book, which tells us that if a quadrilateral is a parallelogram, then its diagonals bisect each other.
Therefore, the following segments are congruent.
AT ≅ TC and BT ≅ TD
By the definition of congruent segments, we can conclude that their lengths are equal.
AT = TC and BT = TD
Let's create a system of equations by substituting the lengths of the segments into these equations.
3y-3=3x 4x-2=3y-1
To solve it we will use the Substitution Method.
