Question

The coordinates of the vertices for the figure HIJK are
HO, 5), (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.
v and the midpoint of IK is
The midpoint of HJ is
(2, 2).
Therefore, HIJK is a parallelogram because the
diagonals
v, which means
they bisect each other.​

Answer 1

Given : the converse of the parallelogram diagonal theorem.

if the diagonals of a quadrilaterals bisects each other , then the

quadrilateral is a parallelogram.

The coordinates of the vertices for the figure HIJK are

H(0, 5), I (3, 3), J(4, -1), and K(1, 1).

To Find :  Check whether HIJK is a parallogram or not

Solution:

H(0, 5), I (3, 3), J(4, -1), and K(1, 1).

Diagonal  HJ  & IK

Mid point of HI

= (0 + 4)/2 , (5 -1)/2

= 2 , 2

Mid point of IK

= (3 + 1)/2 , (3 + 1)/2

= 2,2

Mid point of both Diagonals  is same

Hence Diagonal bisect each other

=> HIJK is a parallelogram

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