Parallelogram Verification: Comparing Sides x+5 and 2x+9

In a parallelogram, we know that each pair of opposite sides are equal to each other.

The data shows that only one pair of sides are equal to each other:

$AB=DC=8$

Now we try to see that the additional pair of sides are equal to each other.

We replace$x=8$for each of the sides:

$AD=2\times8+9$

$AD=16+9$

$AD=25$

$BC=8+5$

$BC=13$

That is, we find that the pair of opposite sides are not equal to each other:

$25\ne13$

Therefore, the quadrilateral is not a parallelogram.