Question

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.

Answer 1

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

Step-by-step explanation:

Answer 2

Answer: The quadrilateral HIJK is a parallelogram.

Step-by-step 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.

`\text{Midpoint of HJ}=((0+4)/(2), (5-1)/(2))`

`\text{Midpoint of HJ}=(2,2)`

Now, find the midpoint of IK.

`\text{Midpoint of IK}=((3+1)/(2), (3+1)/(2))`

`\text{Midpoint of IK}=(2,2)`

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.