Question

select the correct answer.
ac and bd are diagonals of quadrilateral abcd. is quadrilateral abcd a parallelogram? explain
a. yes, because the sides are congruent.
b. no, because the sides are congruent.
c. yes, because the diagonals bisect each other.
d. no, because the diagonals bisect each other.

Explanation:

Step1: Recall the property of parallelogram

One of the properties of a parallelogram is that the diagonals bisect each other. In the given figure, if \(AO = OC\) and \(BO=OD\), then the diagonals bisect each other.
We have \(AO = 4\), \(OC = 4\), \(BO = 6\), \(OD = 6\). So, \(AO=OC\) and \(BO = OD\).

Step2: Apply the theorem

According to the theorem, if the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Answer:

C. Yes, because the diagonals bisect each other.