Recall the theorem that states if a quadrilateral is a parallelogram, then its diagonals bisect each other.
y=5, z=2
Practice makes perfect
We want to find the values of y and z for which JKLM is a parallelogram, 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.
JT ≅ TL and MT ≅ TK
By the definition of congruent segments, we can conclude that their lengths are equal.
JT = TL and MT = TK
Let's create two equations by substituting the lengths of the segments into these equations.
3y - 5 = y + 5 and z + 9 = 2z + 7
Let's start by solving the first equation for y.
