Question

1. if dh = 3x - 3 and fh = x + 7, find the value of x for which defg must be a parallelogram.

o 5
o 2
o 4
o 7

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, $DH = FH$.

Step2: Set up the equation

We have $3x - 3=x + 7$.

Step3: Solve for $x$

Subtract $x$ from both sides: $3x - x-3=x - x + 7$, which simplifies to $2x-3 = 7$. Then add 3 to both sides: $2x-3 + 3=7 + 3$, getting $2x=10$. Divide both sides by 2: $\frac{2x}{2}=\frac{10}{2}$, so $x = 5$.

Answer:

5