Question

which statement proves that quadrilateral jklm is a kite?
∠m is a right angle and mk bisects ∠lmj.
lm = jm = 3 and jk = lk = √17.
mk intersects lj at its mid - point.
the slope of mk is - 1 and the slope of lj is 1.

Explanation:

Step1: Recall kite - definition

A kite is a quadrilateral with two pairs of adjacent sides equal.

Step2: Analyze each option

• Option 1: Just having a right - angle and an angle bisector does not prove it's a kite.
• Option 2: If \(LM = JM=3\) and \(JK = LK=\sqrt{17}\), we have two pairs of adjacent sides equal, which satisfies the definition of a kite.
• Option 3: A line intersecting another at its mid - point does not prove the quadrilateral is a kite.
• Option 4: Perpendicular diagonals do not necessarily mean the quadrilateral is a kite.

Answer:

LM = JM = 3 and JK = LK = \(\sqrt{17}\)