Question

if $eg = 2z + 13$ and $ei = 6z + 1$, find $eg$ in parallelogram $fghi$.

Explanation:

Step1: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $EG = EI$.

Step2: Set up equation and solve for $z$

$$2z + 13 = 6z + 1$$
$$13 - 1 = 6z - 2z$$
$$12 = 4z$$
$$z = \frac{12}{4} = 3$$

Step3: Substitute $z$ into $EG$ expression

$$EG = 2(3) + 13$$

Answer:

19