Parallelogram Property Investigation: Proving AO = OC in a Quadrilateral

Look at the quadrilateral below.

AO = OC

Is it a parallelogram?

Let's pay attention to the diagonals, remember that in a parallelogram the diagonals intersect each other.

Therefore, we will find AO, OC, BO, DO and check if they are equal and intersect each other.

We refer to the figure:

$AO=OC$

$9x+1=10x$

We place like terms:

$1=10x-9x$

$1=x$

We replace:

$AO=9\times1+1=10$

$OC=10\times1=10$

Now we know that indeed$AO=OC$

Now we establish that X=1 and see if BO is equal to OD:

$BO=3x-2$

$BO=3\times1-2=$

$BO=3-2=1$

$OD=5x+4$

$OD=5\times1+4$

$OD=5+4=9$

Now we find that: $BO\ne OD$

Since the diagonals do not intersect each other, the quadrilateral is not a parallelogram.