The coordinates of the vertices for the figure hijk are h(0, 5), i(3, 3), j(4, –1), and k(1, 1). to determine if it is a parallelogram, use the converse of the parallelogram diagonal theorem. this states that if the diagonals , then the quadrilateral is a parallelogram. the midpoint of hj is and the midpoint of ik is (2, 2). therefore, hijk is a parallelogram because the diagonals , which means they bisect each other.

IH = IJ = 3 and JK = HK = StartRoot 29 EndRoot, and IH ≠ JK and IJ ≠ HK.

Step-by-step explanation:

The quadrilateral HIJK is a parallelogram.

Explanation:

It is given that the coordinates of the vertices for the figure HIJK are H(0, 5), I(3, 3), J(4, –1), and K(1, 1).

The parallelogram diagonal theorem states that  the quadrilateral is a parallelogram if both diagonal bisects each other.

If HIJK is a quadrilateral, then HJ and IK are the diagonals of HIJK.

First we find the midpoint of HJ.

Now, find the midpoint of IK.

The midpoint of both diagonal are same. It means the diagonals of HIJK bisects each other.

By parallelogram diagonal theorem, we can say that the quadrilateral HIJK is a parallelogram.

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step-by-step explanation: