Question

if $vx = a + 14$ and $vz = 15a$, find the value of $a$ that makes quadrilateral $wxyz$ a parallelogram.

Explanation:

Step1: Set segments equal (diag. bisect)

In a parallelogram, diagonals bisect each other, so $VX = VZ$.
Substitute given expressions: $a + 14 = 15a$

Step2: Isolate variable $a$

Subtract $a$ from both sides: $14 = 15a - a$
Simplify right-hand side: $14 = 14a$

Step3: Solve for $a$

Divide both sides by 14: $\frac{14}{14} = \frac{14a}{14}$
Simplify: $1 = a$

Answer:

$a = 1$