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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 of the diagonals, which means they bisect each other.

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Answer:

In ΔHKJ and ΔHIJ

HK=IJ=√17

HI=KJ=√13

HJ=HJ [Common}

ΔHKJ ≅ ΔHIJ [SSS]

Now consider ΔHKI AND ΔKJI

HK=IJ=√17

HI=KJ=√13

KI=KI [Common]

ΔHKI ≅ ΔKJI [SSS]

Now the converse of Parallelogram diagonal theorem also states that if diagonals of a Quadrilateral divides it into two congruent triangles then it is a parallelogram.

Hence the given Quadrilateral is a Parallelogram.

Step-by-step explanation:

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