Classifying a Quadrilateral in the Coordinate Plane

Which statement proves that quadrilateral HIJK is a kite?
HI ⊥ IJ, and m∠H = m∠J.
IH = IJ = 3 and JK = HK = , and IH ≠ JK and IJ ≠ HK.
IK intersects HJ at the midpoint of HJ at (−1.5, 2.5).
The slope of HK = and the slope of JK = .

A kite is a quadrilateral (has four sides and four angles) in which adjacent sides are congruent. A kite also has a pair of opposite angles and the diagonals bisect each other.

Given that quadrilateral HIJK is a kite. HI and IJ are adjacent sides while JK and HK are adjacent sides. Since adjacent sides are congruent:

IH = IJ = 3 and JK = HK = √29, and IH ≠ JK and IJ ≠ HK proves that quadrilateral HIJK is a kite.

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Classifying a Quadrilateral in the Coordinate Plane Which statement proves that quadrilateral HIJK is a kite? HI ⊥ IJ, and m∠H = m∠J. IH = IJ = 3 and JK = HK = , and IH ≠ JK and IJ ≠ HK. IK intersects HJ at the midpoint of HJ at (−1.5, 2.5). The slope of HK = and the slope of JK = .

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What is a kite?

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Classifying a Quadrilateral in the Coordinate Plane

Which statement proves that quadrilateral HIJK is a kite?
HI ⊥ IJ, and m∠H = m∠J.
IH = IJ = 3 and JK = HK = , and IH ≠ JK and IJ ≠ HK.
IK intersects HJ at the midpoint of HJ at (−1.5, 2.5).
The slope of HK = and the slope of JK = .